diff --git a/crates/content/src/lib.rs b/crates/content/src/lib.rs
index fb17a903d1..f77c54e1dc 100644
--- a/crates/content/src/lib.rs
+++ b/crates/content/src/lib.rs
@@ -58,6 +58,23 @@ impl Op {
     pub fn last_name(&self) -> Option<&[u8]> {
         self.operands.last().and_then(Object::as_name)
     }
+
+    /// Operand `k` counted from the end (0 is the last), as the renderer reads an operator's
+    /// operands: `(x) /OC /MC0 BDC` marks with `/OC /MC0`, and `(x) /F1 10 Tf` selects `/F1`.
+    pub fn back(&self, k: usize) -> Option<&Object> {
+        let i = self.operands.len().checked_sub(k)?.checked_sub(1)?;
+        self.operands.get(i)
+    }
+
+    /// [`Op::back`] as a name.
+    pub fn name_back(&self, k: usize) -> Option<&[u8]> {
+        self.back(k).and_then(Object::as_name)
+    }
+
+    /// [`Op::back`] as a number.
+    pub fn num_back(&self, k: usize) -> Option<f64> {
+        self.back(k).and_then(Object::as_f64)
+    }
 }
 
 /// A parsed stream.
diff --git a/crates/content/src/tests.rs b/crates/content/src/tests.rs
index 9ca12c4536..89f258853d 100644
--- a/crates/content/src/tests.rs
+++ b/crates/content/src/tests.rs
@@ -10,6 +10,17 @@ thread_local! {
     pub(crate) static PIECE_VISITS: std::cell::Cell<usize> = const { std::cell::Cell::new(0) };
 }
 
+#[test]
+fn operands_are_counted_from_the_end() {
+    let op = parse(b"(x) /OC /MC0 BDC").ops.remove(0);
+    assert_eq!((op.name_back(1), op.name_back(0)), (Some(&b"OC"[..]), Some(&b"MC0"[..])));
+    assert_eq!(op.back(2).and_then(Object::as_string).map(|s| s.bytes.clone()), Some(b"x".to_vec()));
+    assert_eq!((op.back(3), op.back(usize::MAX)), (None, None));
+    let op = parse(b"/F1 10 Tf").ops.remove(0);
+    assert_eq!((op.name_back(1), op.num_back(0), op.num_back(1)), (Some(&b"F1"[..]), Some(10.0), None));
+    assert_eq!(Op::new("Q", vec![]).back(0), None);
+}
+
 #[test]
 fn splicing_visits_each_piece_a_few_times() {
     let n = 5_000;
diff --git a/crates/redact/src/interp.rs b/crates/redact/src/interp.rs
index 9cfc981381..7a4adb1f0e 100644
--- a/crates/redact/src/interp.rs
+++ b/crates/redact/src/interp.rs
@@ -571,7 +571,12 @@ impl Walk {
                 Some(op)
             }
             b"cs" | b"CS" => {
-                if op.name(0) != Some(b"Pattern") {
+                // A Pattern space is told by the name `/Pattern` alone: one named through the
+                // resources' `/ColorSpace` clears the pattern, which the app's renderer keeps and
+                // Poppler doesn't (`cs` resets the colour, ISO 32000-2 §8.6.8). Looking the name up
+                // at each `cs` wants a cache for the page: a `/ColorSpace` too large for the
+                // document to keep is parsed again at each read.
+                if op.last_name() != Some(b"Pattern") {
                     if o == b"cs" {
                         self.gs.fill_pattern = None;
                     } else {
@@ -598,8 +603,12 @@ impl Walk {
         let o = op.op.as_slice();
         let pts: Vec<(f64, f64)> = match o {
             b"re" => op.nums::<4>().map(|[x, y, w, h]| vec![(x, y), (x + w, y), (x, y + h), (x + w, y + h)]).unwrap_or_default(),
-            b"h" | b"W" | b"W*" => Vec::new(),
-            _ => op.operands.iter().filter_map(Object::as_f64).collect::<Vec<_>>().as_chunks::<2>().0.iter().map(|p| (p[0], p[1])).collect(),
+            // Each takes its points from the end, as the renderer reads them: a surplus before
+            // them is ignored, not read as a point.
+            b"m" | b"l" => op.nums::<2>().map(|[x, y]| vec![(x, y)]).unwrap_or_default(),
+            b"c" => op.nums::<6>().map(|[x1, y1, x2, y2, x3, y3]| vec![(x1, y1), (x2, y2), (x3, y3)]).unwrap_or_default(),
+            b"v" | b"y" => op.nums::<4>().map(|[x1, y1, x2, y2]| vec![(x1, y1), (x2, y2)]).unwrap_or_default(),
+            _ => Vec::new(),
         };
         for (x, y) in pts {
             let (u, v) = self.gs.ctm.apply(x, y);
@@ -656,10 +665,10 @@ impl Walk {
             }
             b"Tf" => self.select_font(doc, scope, op),
             _ => {
-                if let Some((font, vertical, size)) = op.name(0).and_then(|n| extgstate_font(doc, scope, &self.ext_gstates, n, &self.fallback)) {
+                if let Some((font, vertical, size)) = op.last_name().and_then(|n| extgstate_font(doc, scope, &self.ext_gstates, n, &self.fallback)) {
                     (self.gs.font, self.gs.vertical, self.gs.size) = (font, vertical, size);
                     // As for `Tf`: a Type 3 font without /Resources paints through this scope's.
-                    self.gs.type3_inherits = op.name(0).is_some_and(|n| extgstate_type3_inherits(doc, &self.ext_gstates, n));
+                    self.gs.type3_inherits = op.last_name().is_some_and(|n| extgstate_type3_inherits(doc, &self.ext_gstates, n));
                 }
             }
         }
@@ -864,7 +873,8 @@ fn clean_replacements(
             if !op.is("BDC") || !affected.contains(&op.span.start) {
                 continue;
             }
-            let property = match op.operands.get(1) {
+            // The property list is the last operand, as the renderer reads it.
+            let property = match op.back(0) {
                 Some(Object::Name(name)) => properties.get(name).map(|p| doc.resolve(p)),
                 Some(p) => Some(doc.resolve(p)),
                 None => None,
@@ -874,7 +884,7 @@ fn clean_replacements(
                 for key in [&b"ActualText"[..], b"Alt", b"E", b"T"] {
                     stripped |= dict.remove(key).is_some();
                 }
-                if stripped && let Some(property) = op.operands.get_mut(1) {
+                if stripped && let Some(property) = op.operands.last_mut() {
                     *property = Object::Dict(dict);
                     *changed = true;
                     report.replacement_text += 1;
diff --git a/crates/redact/src/interp/layers.rs b/crates/redact/src/interp/layers.rs
index 88d1c4e677..362cb36620 100644
--- a/crates/redact/src/interp/layers.rs
+++ b/crates/redact/src/interp/layers.rs
@@ -225,8 +225,10 @@ pub(super) fn strip_hidden_layers(doc: &Document, scope: &mut Scope<'_>, ops: Ve
         match op.op.as_slice() {
             b"BDC" | b"BMC" => {
                 let this = op.is("BDC")
-                    && op.name(0) == Some(b"OC")
-                    && match op.operands.get(1) {
+                    // The tag and the property list are the last two operands, as the renderer
+                    // reads them: `(x) /OC /MC0 BDC` is a layer's block too.
+                    && op.name_back(1) == Some(b"OC")
+                    && match op.back(0) {
                         Some(Object::Name(n)) => props.get(n).is_some_and(|o| scope.layer_hidden(doc, o)),
                         Some(o) => scope.layer_hidden(doc, o),
                         None => false,
diff --git a/crates/redact/src/interp/prune.rs b/crates/redact/src/interp/prune.rs
index 43cc886826..254d0c7a06 100644
--- a/crates/redact/src/interp/prune.rs
+++ b/crates/redact/src/interp/prune.rs
@@ -358,7 +358,7 @@ fn prune_retired_properties(doc: &Document, res: &mut Dict, names: &[Vec<u8>], c
         // Each is one page's content or one form's, with the allowance of a page.
         for op in resource_ops(doc, &mut DecodeBudget::page(), res, content)? {
             if matches!(op.op.as_slice(), b"BDC" | b"DP")
-                && let Some(name) = op.name(1)
+                && let Some(name) = op.last_name()
             {
                 used.insert(name.to_vec());
             }
@@ -522,7 +522,7 @@ pub(crate) fn prune_properties(doc: &Document, budget: &mut DecodeBudget, res: &
     let ops = resource_ops(doc, budget, res, content)?;
     let names: Vec<Vec<u8>> = properties.iter().map(|(n, _)| n.to_vec()).collect();
     for name in names {
-        if !ops.iter().any(|op| matches!(op.op.as_slice(), b"BDC" | b"DP") && op.name(1) == Some(&name))
+        if !ops.iter().any(|op| matches!(op.op.as_slice(), b"BDC" | b"DP") && op.last_name() == Some(&name))
             && let Some(value) = properties.remove(&name)
         {
             retired.push(value);
diff --git a/crates/redact/src/tags.rs b/crates/redact/src/tags.rs
index 648c0c29e5..03573a9743 100644
--- a/crates/redact/src/tags.rs
+++ b/crates/redact/src/tags.rs
@@ -35,6 +35,14 @@ impl Marked {
 /// left are taken as changed (their descriptions go) rather than compared.
 const MAX_COMPARED: usize = 1 << 28;
 
+/// `f` of `o`, or of the object it refers to, without copying a direct one.
+fn with_held<R>(doc: &Document, o: &Object, f: impl FnOnce(&Object) -> R) -> R {
+    match o {
+        Object::Ref(_) => f(&doc.resolve(o)),
+        o => f(o),
+    }
+}
+
 fn by_mcid(doc: &Document, resources: &Dict, data: &[u8]) -> Marked {
     let mut out = Marked::default();
     // Open sequences: the MCID with where its content starts in `ops` and the drawing operators
@@ -49,14 +57,22 @@ fn by_mcid(doc: &Document, resources: &Dict, data: &[u8]) -> Marked {
             e.1 |= drawn > drawn_before;
         }
     };
+    // The named property lists, read once, and each name's MCID, read once: a stream can name one
+    // at every `BDC` of thousands, and reading an object again can parse it again, all of it (the
+    // document keeps an object larger than its cache only until it reads another). A direct one
+    // is read where it is.
+    let held = resources.get(b"Properties").filter(|p| matches!(p, Object::Ref(_))).map(|p| doc.resolve(p));
+    let named = held.as_deref().or_else(|| resources.get(b"Properties")).and_then(Object::as_dict);
+    let mut mcids: HashMap<Vec<u8>, Option<i64>> = HashMap::new();
     for op in pdfcraft_content::parse(data).ops {
         match op.op.as_slice() {
             b"BDC" => {
-                let id = match op.operands.get(1) {
-                    Some(Object::Name(n)) => resources.get(b"Properties").and_then(|p| {
-                        let props = doc.resolve(p);
-                        let prop = doc.resolve(props.as_dict()?.get(n)?);
-                        prop.as_dict()?.int(b"MCID")
+                // The property list is the last operand, as the renderer reads it.
+                let id = match op.back(0) {
+                    Some(Object::Name(n)) => *mcids.entry(n.to_vec()).or_insert_with(|| {
+                        let prop = named?.get(n)?;
+                        // A named property list may give its MCID by reference.
+                        with_held(doc, prop, |prop| prop.as_dict()?.get(b"MCID").and_then(|id| with_held(doc, id, Object::as_int)))
                     }),
                     Some(p) => doc.resolve(p).as_dict().and_then(|d| d.int(b"MCID")),
                     _ => None,
@@ -86,9 +102,7 @@ fn by_mcid(doc: &Document, resources: &Dict, data: &[u8]) -> Marked {
         }
         let draws = match op.op.as_slice() {
             b"Tj" | b"'" | b"\"" => op.operands.last().and_then(Object::as_string).is_some_and(|s| !s.bytes.is_empty()),
-            b"TJ" => {
-                op.operands.first().and_then(Object::as_array).is_some_and(|a| a.iter().any(|x| x.as_string().is_some_and(|s| !s.bytes.is_empty())))
-            }
+            b"TJ" => op.back(0).and_then(Object::as_array).is_some_and(|a| a.iter().any(|x| x.as_string().is_some_and(|s| !s.bytes.is_empty()))),
             b"f" | b"F" | b"f*" | b"B" | b"B*" | b"b" | b"b*" | b"S" | b"s" | b"sh" | b"Do" | b"BI" => true,
             _ => false,
         };
@@ -139,7 +153,7 @@ fn mcid_of(doc: &Document, o: &Object, page: Option<ObjRef>, target: ObjRef, str
         Object::Dict(m) if m.name(b"Type") == Some(b"MCR") => {
             let pg = m.get(b"Pg").and_then(Object::as_ref).or(page);
             let stm = m.get(b"Stm").and_then(Object::as_ref);
-            (pg == Some(target) && stm == stream.map(|s| s.0)).then(|| m.int(b"MCID")).flatten()
+            (pg == Some(target) && stm == stream.map(|s| s.0)).then(|| m.get(b"MCID").and_then(|id| doc.resolve(id).as_int())).flatten()
         }
         _ => None,
     }
diff --git a/crates/redact/src/tests.rs b/crates/redact/src/tests.rs
index 0e611c6678..3cf25f9b78 100644
--- a/crates/redact/src/tests.rs
+++ b/crates/redact/src/tests.rs
@@ -6238,6 +6238,7 @@ mod inline_images;
 mod limits;
 mod metadata_fail_closed;
 mod metadata_matching;
+mod operands_from_the_end;
 mod property_retirement;
 mod surviving_references;
 mod text_state;
diff --git a/crates/redact/src/tests/operands_from_the_end.rs b/crates/redact/src/tests/operands_from_the_end.rs
new file mode 100644
index 0000000000..0c802763e9
--- /dev/null
+++ b/crates/redact/src/tests/operands_from_the_end.rs
@@ -0,0 +1,340 @@
+//! An operator takes its operands from the end, as the renderer reads them, and a surplus before
+//! them is ignored: `(x) /OC /MC0 BDC` marks a layer's block, `(x) /GS1 gs` selects `/GS1`. Read
+//! from the front, the surplus stood in for the operands, and what they named went unseen.
+
+use super::*;
+
+/// Hidden-layer text in a block whose tag and property list follow a string: Remove Hidden
+/// Information found nothing to remove, and the text stayed.
+#[test]
+fn a_hidden_layers_block_after_a_surplus_operand_is_removed() {
+    use crate::sanitize::{Hidden, remove_hidden};
+    let mut doc = one_page(
+        b"(x) /OC /MC0 BDC BT /F1 10 Tf 20 260 Td (LAYERSECRET) Tj ET EMC BT /F1 10 Tf 20 20 Td (PUBLIC) Tj ET",
+        "/Properties << /MC0 7 0 R >>",
+        vec![b"<< /Type /OCG /Name (Hidden) >>".to_vec()],
+    );
+    doc.update_dict(ObjRef::new(1, 0), |d| {
+        d.set(
+            b"OCProperties".to_vec(),
+            Object::Dict(Dict::from_iter([
+                (b"OCGs".to_vec(), Object::Array(vec![Object::Ref(ObjRef::new(7, 0))])),
+                (b"D".to_vec(), Object::Dict(Dict::from_iter([(b"OFF".to_vec(), Object::Array(vec![Object::Ref(ObjRef::new(7, 0))]))]))),
+            ])),
+        );
+    })
+    .unwrap();
+    let removed = remove_hidden(&mut doc, &[Hidden::HiddenLayers]);
+    assert!(removed.as_ref().is_ok_and(|r| r.iter().any(|(h, n)| *h == Hidden::HiddenLayers && *n > 0)), "{removed:?}");
+    let c = content(&doc, 0);
+    assert!(!c.contains("LAYERSECRET") && c.contains("PUBLIC"), "{c}");
+}
+
+/// Paint under a mark named by `/ActualText` in a block after a surplus operand: the name, which
+/// would still read the word, kept it.
+#[test]
+fn actual_text_after_a_surplus_operand_goes_with_the_paint_it_names() {
+    let mut doc = one_page(b"(x) /Span <</ActualText (SECRET)>> BDC 100 100 m 160 100 l 160 120 l 100 120 l h f EMC", "", vec![]);
+    mark(&mut doc, 0, &[[90.0, 95.0, 130.0, 125.0]], "");
+    let r = apply(&mut doc, None).unwrap();
+    assert_eq!(r.paths_removed, 1);
+    let c = content(&doc, 0);
+    assert!(!c.contains("SECRET"), "{c}");
+}
+
+/// A tagged paragraph whose `MCID` follows a surplus operand: its structure element kept the
+/// removed text in `/ActualText` and `/Alt`.
+#[test]
+fn a_tag_after_a_surplus_operand_loses_what_redaction_removed() {
+    let content = b"(x) /P <</MCID 0>> BDC BT /F1 10 Tf 10 200 Td (SECRET) Tj ET EMC";
+    let mut doc = pdf(vec![
+        b"<< /Type /Catalog /Pages 2 0 R /StructTreeRoot 7 0 R /MarkInfo << /Marked true >> >>".to_vec(),
+        b"<< /Type /Pages /Kids [3 0 R] /Count 1 >>".to_vec(),
+        b"<< /Type /Page /Parent 2 0 R /MediaBox [0 0 300 300] /Contents 4 0 R /StructParents 0 /Resources << /Font << /F1 5 0 R >> >> >>".to_vec(),
+        stream("", content),
+        FONT.replace("95 0 R", "6 0 R").into_bytes(),
+        widths(),
+        b"<< /Type /StructTreeRoot /K 8 0 R >>".to_vec(),
+        b"<< /S /Document /P 7 0 R /K [9 0 R] >>".to_vec(),
+        b"<< /S /P /P 8 0 R /Pg 3 0 R /ActualText (SECRET) /Alt (the secret) /K 0 >>".to_vec(),
+    ]);
+    mark(&mut doc, 0, &[[5.0, 195.0, 60.0, 212.0]], "");
+    assert_eq!(apply(&mut doc, None).unwrap().tags, 1);
+    let secret = doc.get(ObjRef::new(9, 0)).as_dict().cloned().unwrap();
+    assert!(secret.get(b"ActualText").is_none() && secret.get(b"Alt").is_none(), "{secret:?}");
+}
+
+/// A property list still drawn with, named after a surplus operand, stays in the page's resources
+/// when the redaction cleans them; read from the front, it was taken for unused and retired.
+#[test]
+fn a_property_list_named_after_a_surplus_operand_is_kept() {
+    let mut doc = one_page(
+        b"BT /F1 10 Tf 20 260 Td (SECRET) Tj ET (x) /Span /Pr1 BDC BT /F1 10 Tf 20 20 Td (KEPT) Tj ET EMC",
+        "/Properties << /Pr1 << /Lang (en-GB) >> >>",
+        vec![],
+    );
+    mark(&mut doc, 0, &[[0.0, 200.0, 300.0, 300.0]], "");
+    assert_eq!(apply(&mut doc, None).unwrap().glyphs, 6);
+    let page = pdfcraft_model::pages(&doc).swap_remove(0);
+    let res = page.dict.get(b"Resources").map(|r| doc.resolve(r)).and_then(|r| r.as_dict().cloned()).unwrap_or_default();
+    let props = res.get(b"Properties").map(|p| doc.resolve(p)).and_then(|p| p.as_dict().cloned()).unwrap_or_default();
+    assert!(props.contains(b"Pr1"), "{res:?}");
+}
+
+/// A font set only by an ExtGState selected after a surplus operand: read from the front, no font
+/// was set, every glyph stood at the start of the line with no size, and a mark over the end of
+/// the word removed nothing.
+#[test]
+fn a_font_from_an_extgstate_selected_after_a_surplus_operand_places_the_text() {
+    let mut doc = one_page(b"BT (x) /GS1 gs 20 260 Td (SECRET) Tj ET", "/ExtGState << /GS1 << /Font [5 0 R 10] >> >>", vec![]);
+    // Over the last two glyphs, E and T at x = 40 to 50.
+    mark(&mut doc, 0, &[[42.0, 255.0, 55.0, 275.0]], "");
+    assert_eq!(apply(&mut doc, None).unwrap().glyphs, 2);
+}
+
+/// `/Pattern cs` after a surplus operand, once the pattern's paint under the mark went: it selects
+/// the Pattern space and keeps the pattern, so the fill after it still counts as painting with it
+/// and the pattern stays. Read from the front, the surplus cleared the pattern, which was pruned.
+/// A grey space clears it.
+#[test]
+fn a_pattern_space_selected_after_a_surplus_operand_keeps_the_pattern() {
+    for (space, pruned) in [("(x) /Pattern", 0), ("/Pattern", 0), ("(x) /DeviceGray", 1)] {
+        let mut doc = one_page(
+            format!("/Pattern cs /P0 scn 10 260 20 20 re f {space} cs 200 20 50 50 re f").as_bytes(),
+            "/Pattern << /P0 7 0 R >>",
+            vec![stream("/PatternType 1 /PaintType 1 /TilingType 1 /BBox [0 0 10 10] /XStep 10 /YStep 10 /Resources << >>", b"0 0 5 5 re f")],
+        );
+        mark(&mut doc, 0, &[[0.0, 250.0, 40.0, 290.0]], "");
+        let r = apply(&mut doc, None).unwrap();
+        assert_eq!((r.paths_removed, r.patterns_removed), (1, pruned), "{space}");
+    }
+}
+
+/// A Type 3 font selected after a surplus operand, outside the mark, whose glyph selects an
+/// ExtGState, a colour space, a property list and a font after one too: the cleanups after the
+/// walk took the font for undrawn and those for unused. All stay, with the glyph.
+#[test]
+fn a_type3_font_and_its_glyphs_resources_named_after_a_surplus_operand_are_kept() {
+    let mut doc = pdf(vec![
+        b"<< /Type /Catalog /Pages 2 0 R >>".to_vec(),
+        b"<< /Type /Pages /Kids [3 0 R] /Count 1 >>".to_vec(),
+        b"<< /Type /Page /Parent 2 0 R /MediaBox [0 0 300 300] /Contents 4 0 R /Resources << /Font << /F1 5 0 R /T3 7 0 R >> >> >>".to_vec(),
+        stream("", b"BT /F1 10 Tf 20 260 Td (SECRET) Tj ET BT (x) /T3 12 Tf 20 20 Td (a) Tj ET"),
+        FONT.replace("95 0 R", "6 0 R").into_bytes(),
+        widths(),
+        b"<< /Type /Font /Subtype /Type3 /FontBBox [0 0 10 10] /FontMatrix [0.1 0 0 0.1 0 0] /CharProcs << /a 8 0 R >> \
+           /Encoding << /Differences [97 /a] >> /FirstChar 97 /LastChar 97 /Widths [10] /Resources << /ExtGState << /GS0 << /CA 0.5 >> >> \
+           /ColorSpace << /CS0 /DeviceGray >> /Properties << /P0 << >> >> /Font << /F0 5 0 R >> >> >>"
+            .to_vec(),
+        stream("", b"10 0 d0 (x) /GS0 gs (x) /CS0 cs (x) /Span /P0 BDC 0 0 10 10 re f EMC BT (x) /F0 1 Tf ET"),
+    ]);
+    mark(&mut doc, 0, &[[0.0, 200.0, 300.0, 300.0]], "");
+    assert_eq!(apply(&mut doc, None).unwrap().glyphs, 6);
+    let page = pdfcraft_model::pages(&doc).swap_remove(0);
+    let res = page.dict.get(b"Resources").map(|r| doc.resolve(r)).and_then(|r| r.as_dict().cloned()).unwrap_or_default();
+    let fonts = res.get(b"Font").map(|f| doc.resolve(f)).and_then(|f| f.as_dict().cloned()).unwrap_or_default();
+    let font = fonts.get(b"T3").map(|f| doc.resolve(f)).and_then(|f| f.as_dict().cloned());
+    let font = font.unwrap_or_else(|| panic!("the drawn Type 3 font stays: {fonts:?}"));
+    let procs = font.get(b"CharProcs").map(|p| doc.resolve(p)).and_then(|p| p.as_dict().cloned()).unwrap_or_default();
+    assert!(procs.contains(b"a"), "its glyph stays: {font:?}");
+    let font_res = font.get(b"Resources").map(|r| doc.resolve(r)).and_then(|r| r.as_dict().cloned()).unwrap_or_default();
+    let states = font_res.get(b"ExtGState").map(|s| doc.resolve(s)).and_then(|s| s.as_dict().cloned()).unwrap_or_default();
+    assert!(states.contains(b"GS0"), "the ExtGState its glyph selects stays: {font_res:?}");
+    for (kind, name) in [(&b"ColorSpace"[..], &b"CS0"[..]), (b"Properties", b"P0"), (b"Font", b"F0")] {
+        let held = font_res.get(kind).map(|d| doc.resolve(d)).and_then(|d| d.as_dict().cloned()).unwrap_or_default();
+        assert!(held.contains(name), "the {} its glyph uses stays: {font_res:?}", String::from_utf8_lossy(name));
+    }
+}
+
+/// A tagged paragraph whose `TJ` after a surplus operand still draws once the mark has removed the
+/// word beside it: read from the front, that `TJ` drew nothing, the paragraph was taken for empty,
+/// and its structure element lost the content the page still shows.
+#[test]
+fn a_tagged_tj_after_a_surplus_operand_still_draws() {
+    let content = b"/P <</MCID 0>> BDC BT /F1 10 Tf 10 200 Td (SECRET) Tj 10 -100 Td (x) [(KEPT)] TJ ET EMC";
+    let mut doc = pdf(vec![
+        b"<< /Type /Catalog /Pages 2 0 R /StructTreeRoot 7 0 R /MarkInfo << /Marked true >> >>".to_vec(),
+        b"<< /Type /Pages /Kids [3 0 R] /Count 1 >>".to_vec(),
+        b"<< /Type /Page /Parent 2 0 R /MediaBox [0 0 300 300] /Contents 4 0 R /StructParents 0 /Resources << /Font << /F1 5 0 R >> >> >>".to_vec(),
+        stream("", content),
+        FONT.replace("95 0 R", "6 0 R").into_bytes(),
+        widths(),
+        b"<< /Type /StructTreeRoot /K 8 0 R >>".to_vec(),
+        b"<< /S /Document /P 7 0 R /K [9 0 R] >>".to_vec(),
+        b"<< /S /P /P 8 0 R /Pg 3 0 R /K 0 >>".to_vec(),
+    ]);
+    mark(&mut doc, 0, &[[5.0, 195.0, 60.0, 212.0]], "");
+    assert_eq!(apply(&mut doc, None).unwrap().glyphs, 6);
+    let paragraph = doc.get(ObjRef::new(9, 0)).as_dict().cloned().unwrap();
+    assert_eq!(paragraph.get(b"K").and_then(Object::as_int), Some(0), "it still tags what the page shows: {paragraph:?}");
+}
+
+/// A path's points follow a surplus number: read from the front, each point was shifted by one,
+/// so a square under the mark was placed beside it and kept, and one beside the mark was placed
+/// under it and removed.
+#[test]
+fn a_paths_points_after_a_surplus_number_are_where_the_renderer_draws_them() {
+    let under = b"0 0 1 rg 9 100 100 m 9 140 100 l 9 140 140 l 9 100 140 l h f 9 100 100 m 9 140 140 l S".as_slice();
+    let mut doc = one_page(under, "", vec![]);
+    mark(&mut doc, 0, &[[90.0, 90.0, 150.0, 150.0]], "");
+    assert_eq!(apply(&mut doc, None).unwrap().paths_removed, 2, "both paths under the mark go");
+    let beside =
+        b"0 0 1 rg 0 200 200 m 250 200 l 250 250 l 200 250 l h f 0 200 200 m 210 210 220 220 230 230 c 240 240 250 250 v 200 250 200 260 y h f"
+            .as_slice();
+    let mut doc = one_page(beside, "", vec![]);
+    mark(&mut doc, 0, &[[0.0, 0.0, 20.0, 20.0]], "");
+    assert_eq!(apply(&mut doc, None).unwrap().paths_removed, 0, "the paths beside the mark stay");
+    // Curves whose points, after a surplus, reach under the mark.
+    for curve in [&b"200 200 m 9 10 10 12 12 15 15 c f"[..], b"200 200 m 9 10 10 15 15 v f", b"200 200 m 9 10 10 15 15 y f"] {
+        let mut doc = one_page(curve, "", vec![]);
+        mark(&mut doc, 0, &[[0.0, 0.0, 20.0, 20.0]], "");
+        assert_eq!(apply(&mut doc, None).unwrap().paths_removed, 1, "{}", String::from_utf8_lossy(curve));
+    }
+    // A line, and curves, from a point beside the mark whose points, after a surplus, stay beside
+    // it: read from the front, the surplus was a point under it.
+    for curve in [
+        &b"100 100 500 m 510 510 l S"[..],
+        b"500 500 m 100 100 510 l S",
+        b"100 500 m 100 100 500 110 500 120 500 c f",
+        b"100 500 m 100 110 500 120 500 v f",
+        b"100 500 m 100 110 500 120 500 y f",
+    ] {
+        let mut doc = one_page(curve, "", vec![]);
+        mark(&mut doc, 0, &[[90.0, 90.0, 150.0, 150.0]], "");
+        assert_eq!(apply(&mut doc, None).unwrap().paths_removed, 0, "{}", String::from_utf8_lossy(curve));
+    }
+}
+
+/// An `MCID` given by reference: in a named property list, and in a structure element's `/MCR`.
+/// Read directly, it was missed, and the element kept the removed text.
+#[test]
+fn an_mcid_given_by_reference_loses_what_redaction_removed() {
+    for (content, properties, kid) in [
+        (b"/P /MC0 BDC BT /F1 10 Tf 10 200 Td (SECRET) Tj ET EMC".as_slice(), "/Properties << /MC0 << /MCID 10 0 R >> >>", "0"),
+        (b"/P <</MCID 0>> BDC BT /F1 10 Tf 10 200 Td (SECRET) Tj ET EMC", "", "<< /Type /MCR /Pg 3 0 R /MCID 10 0 R >>"),
+    ] {
+        let mut doc = pdf(vec![
+            b"<< /Type /Catalog /Pages 2 0 R /StructTreeRoot 7 0 R /MarkInfo << /Marked true >> >>".to_vec(),
+            b"<< /Type /Pages /Kids [3 0 R] /Count 1 >>".to_vec(),
+            format!("<< /Type /Page /Parent 2 0 R /MediaBox [0 0 300 300] /Contents 4 0 R /StructParents 0 /Resources << /Font << /F1 5 0 R >> {properties} >> >>").into_bytes(),
+            stream("", content),
+            FONT.replace("95 0 R", "6 0 R").into_bytes(),
+            widths(),
+            b"<< /Type /StructTreeRoot /K 8 0 R >>".to_vec(),
+            b"<< /S /Document /P 7 0 R /K [9 0 R] >>".to_vec(),
+            format!("<< /S /P /P 8 0 R /Pg 3 0 R /ActualText (SECRET) /Alt (the SECRET) /K {kid} >>").into_bytes(),
+            b"0".to_vec(),
+        ]);
+        mark(&mut doc, 0, &[[5.0, 195.0, 60.0, 212.0]], "");
+        assert_eq!(apply(&mut doc, None).unwrap().tags, 1, "{properties}{kid}");
+        let secret = doc.get(ObjRef::new(9, 0)).as_dict().cloned().unwrap();
+        assert!(secret.get(b"ActualText").is_none() && secret.get(b"Alt").is_none(), "{secret:?}");
+    }
+    // An `/MCR` naming the same MCID in a form's stream (`/Stm`) is other content: it stays.
+    let mut doc = pdf(vec![
+        b"<< /Type /Catalog /Pages 2 0 R /StructTreeRoot 7 0 R /MarkInfo << /Marked true >> >>".to_vec(),
+        b"<< /Type /Pages /Kids [3 0 R] /Count 1 >>".to_vec(),
+        b"<< /Type /Page /Parent 2 0 R /MediaBox [0 0 300 300] /Contents 4 0 R /StructParents 0 /Resources << /Font << /F1 5 0 R >> >> >>".to_vec(),
+        stream("", b"/P <</MCID 0>> BDC BT /F1 10 Tf 10 200 Td (SECRET) Tj ET EMC"),
+        FONT.replace("95 0 R", "6 0 R").into_bytes(),
+        widths(),
+        b"<< /Type /StructTreeRoot /K 8 0 R >>".to_vec(),
+        b"<< /S /Document /P 7 0 R /K [9 0 R] >>".to_vec(),
+        b"<< /S /P /P 8 0 R /Pg 3 0 R /ActualText (FORMTEXT) /K << /Type /MCR /Pg 3 0 R /Stm 11 0 R /MCID 10 0 R >> >>".to_vec(),
+        b"0".to_vec(),
+        stream("/Type /XObject /Subtype /Form /BBox [0 0 300 300]", b"/P <</MCID 0>> BDC EMC"),
+    ]);
+    mark(&mut doc, 0, &[[5.0, 195.0, 60.0, 212.0]], "");
+    apply(&mut doc, None).unwrap();
+    let other = doc.get(ObjRef::new(9, 0)).as_dict().cloned().unwrap();
+    assert!(other.get(b"ActualText").is_some(), "{other:?}");
+}
+
+/// The resources of page `page`, resolved.
+fn resources_of(doc: &Document, page: usize) -> Dict {
+    let page = pdfcraft_model::pages(doc).swap_remove(page);
+    page.dict.get(b"Resources").map(|r| doc.resolve(r)).and_then(|r| r.as_dict().cloned()).unwrap_or_default()
+}
+
+/// `dict`'s dictionary `key`, resolved.
+fn dict_in(doc: &Document, dict: &Dict, key: &[u8]) -> Dict {
+    dict.get(key).map(|d| doc.resolve(d)).and_then(|d| d.as_dict().cloned()).unwrap_or_default()
+}
+
+/// A property list a second page sharing the resources names after a surplus operand, once the
+/// first page's block that named it was redacted: read from the front, the second page's name went
+/// unseen and the list was retired from under it.
+#[test]
+fn a_property_list_another_page_names_after_a_surplus_operand_is_kept() {
+    use pdfcraft_cos::Stream;
+    let mut doc = one_page(
+        b"/Span /P0 BDC BT /F1 10 Tf 10 200 Td (SECRET) Tj ET EMC",
+        "/Properties << /P0 7 0 R >>",
+        vec![b"<< /ActualText (SECRET) >>".to_vec()],
+    );
+    let shared = doc.add(Object::Dict(resources_of(&doc, 0)));
+    doc.update_dict(ObjRef::new(3, 0), |d| d.set(b"Resources".to_vec(), Object::Ref(shared))).unwrap();
+    let mut second = doc.get(ObjRef::new(3, 0)).as_dict().cloned().unwrap();
+    let contents = doc.add(Object::Stream(Stream::from_raw(Dict::new(), b"(x) /Span /P0 BDC BT /F1 10 Tf 10 100 Td (Other) Tj ET EMC".to_vec())));
+    second.set(b"Contents".to_vec(), Object::Ref(contents));
+    let second = doc.add(Object::Dict(second));
+    doc.update_dict(ObjRef::new(2, 0), |d| {
+        d.set(b"Kids".to_vec(), Object::Array(vec![Object::Ref(ObjRef::new(3, 0)), Object::Ref(second)]));
+        d.set(b"Count".to_vec(), Object::Int(2));
+    })
+    .unwrap();
+    mark(&mut doc, 0, &[[5.0, 195.0, 60.0, 212.0]], "");
+    apply(&mut doc, Some(&[0])).unwrap();
+    let properties = dict_in(&doc, &resources_of(&doc, 1), b"Properties");
+    assert!(properties.contains(b"P0"), "the second page's property list stays: {properties:?}");
+}
+
+/// A Type 3 font set only by an ExtGState's `/Font`, selected after a surplus operand: read from the
+/// front, the cleanups took it for undrawn, dropped it from the page and unlinked its glyph.
+#[test]
+fn a_type3_font_an_extgstate_selects_after_a_surplus_operand_is_kept() {
+    let mut doc = pdf(vec![
+        b"<< /Type /Catalog /Pages 2 0 R >>".to_vec(),
+        b"<< /Type /Pages /Kids [3 0 R] /Count 1 >>".to_vec(),
+        b"<< /Type /Page /Parent 2 0 R /MediaBox [0 0 300 300] /Contents 4 0 R /Resources << /Font << /F1 5 0 R /T3 7 0 R >> /ExtGState << /GS1 << /Font [7 0 R 12] >> >> >> >>".to_vec(),
+        stream("", b"BT /F1 10 Tf 20 260 Td (SECRET) Tj ET BT (x) /GS1 gs 20 20 Td (a) Tj ET"),
+        FONT.replace("95 0 R", "6 0 R").into_bytes(),
+        widths(),
+        b"<< /Type /Font /Subtype /Type3 /FontBBox [0 0 10 10] /FontMatrix [0.1 0 0 0.1 0 0] /CharProcs << /a 8 0 R /b 9 0 R >> \
+           /Encoding << /Differences [97 /a /b] >> /FirstChar 97 /LastChar 98 /Widths [10 10] >>"
+            .to_vec(),
+        stream("", b"10 0 d0 0 0 10 10 re f"),
+        stream("", b"10 0 d0 0 0 5 5 re f"),
+    ]);
+    mark(&mut doc, 0, &[[0.0, 200.0, 300.0, 300.0]], "");
+    assert_eq!(apply(&mut doc, None).unwrap().glyphs, 6);
+    let fonts = dict_in(&doc, &resources_of(&doc, 0), b"Font");
+    assert!(fonts.contains(b"T3"), "the page still lists the font: {fonts:?}");
+    let font = doc.get(ObjRef::new(7, 0)).as_dict().cloned().unwrap_or_default();
+    let procs = dict_in(&doc, &font, b"CharProcs");
+    assert!(procs.contains(b"a"), "the glyph the page draws stays: {procs:?}");
+}
+
+/// A Type 3 font without resources of its own, set by an ExtGState selected after a surplus operand:
+/// its glyph paints through the page's resources, so it may paint with the page's pattern, which
+/// stays once the page's own fill with it was redacted (the text itself fills with grey). Read from the front, the font was taken
+/// for one with resources, and the pattern was pruned.
+#[test]
+fn a_type3_font_without_resources_an_extgstate_selects_after_a_surplus_operand_keeps_the_pattern() {
+    let mut doc = pdf(vec![
+        b"<< /Type /Catalog /Pages 2 0 R >>".to_vec(),
+        b"<< /Type /Pages /Kids [3 0 R] /Count 1 >>".to_vec(),
+        b"<< /Type /Page /Parent 2 0 R /MediaBox [0 0 300 300] /Contents 4 0 R /Resources << /Font << /F1 5 0 R >> /Pattern << /P0 9 0 R >> /ExtGState << /GS1 << /Font [7 0 R 12] >> >> >> >>".to_vec(),
+        stream("", b"/Pattern cs /P0 scn 10 260 20 20 re f 0 g BT (x) /GS1 gs 150 20 Td (a) Tj ET"),
+        FONT.replace("95 0 R", "6 0 R").into_bytes(),
+        widths(),
+        b"<< /Type /Font /Subtype /Type3 /FontBBox [0 0 10 10] /FontMatrix [0.1 0 0 0.1 0 0] /CharProcs << /a 8 0 R >> \
+           /Encoding << /Differences [97 /a] >> /FirstChar 97 /LastChar 97 /Widths [10] >>"
+            .to_vec(),
+        stream("", b"10 0 d0 /Pattern cs /P0 scn 0 0 10 10 re f"),
+        stream("/PatternType 1 /PaintType 1 /TilingType 1 /BBox [0 0 10 10] /XStep 10 /YStep 10 /Resources << >>", b"0 0 5 5 re f"),
+    ]);
+    mark(&mut doc, 0, &[[0.0, 250.0, 40.0, 290.0]], "");
+    let r = apply(&mut doc, None).unwrap();
+    assert_eq!((r.paths_removed, r.patterns_removed), (1, 0));
+}
diff --git a/crates/redact/src/tests/surviving_references.rs b/crates/redact/src/tests/surviving_references.rs
index 0d171b4008..d02e76832e 100644
--- a/crates/redact/src/tests/surviving_references.rs
+++ b/crates/redact/src/tests/surviving_references.rs
@@ -783,6 +783,37 @@ fn a_type3_font_only_a_soft_mask_without_resources_selects_stays_on_the_page() {
     assert!(saved_first_page_lists_font(&doc, b"T4"), "the page no longer lists the font the soft mask selects");
 }
 
+/// The same soft mask, its ExtGState selected after a surplus operand (`(x) /GS1 gs`), which the
+/// renderer ignores: read from the front, the cleanups never read the group, and dropped the font
+/// it selects and its glyph.
+#[test]
+fn a_type3_font_only_a_soft_mask_selected_after_a_surplus_operand_selects_stays_on_the_page() {
+    let mut doc = pdf(vec![
+        b"<< /Type /Catalog /Pages 2 0 R >>".to_vec(),
+        b"<< /Type /Pages /Kids [3 0 R] /Count 1 >>".to_vec(),
+        b"<< /Type /Page /Parent 2 0 R /MediaBox [0 0 300 300] /Contents 4 0 R /Resources 5 0 R >>".to_vec(),
+        stream("", b"BT /T3 10 Tf 10 100 Td (AC) Tj ET (x) /GS1 gs 150 150 100 100 re f"),
+        b"<< /Font << /T3 6 0 R /T4 7 0 R >> /ExtGState << /GS1 << /Type /ExtGState /SMask << /Type /Mask /S /Luminosity /G 8 0 R >> >> >> >>"
+            .to_vec(),
+        type3_abc(9),
+        type3_abc(12),
+        stream(
+            "/Type /XObject /Subtype /Form /BBox [0 0 300 300] /Group << /S /Transparency /CS /DeviceGray >>",
+            b"1 g BT /T4 40 Tf 160 180 Td (B) Tj ET",
+        ),
+        stream("", b"% REDACTED_GLYPH_A"),
+        stream("", b"% UNUSED_GLYPH_B"),
+        stream("", b"% PAGE_GLYPH_C"),
+        stream("", b"% UNUSED_T4_GLYPH_A"),
+        stream("", b"% MASK_GLYPH_B"),
+        stream("", b"% UNUSED_T4_GLYPH_C"),
+    ]);
+    mark(&mut doc, 0, &[[9.0, 95.0, 14.9, 110.0]], "");
+    assert_eq!(apply(&mut doc, None).unwrap().glyphs, 1);
+    assert!(full_save_holds(&doc, b"MASK_GLYPH_B"), "the glyph the soft mask shows was unlinked");
+    assert!(saved_first_page_lists_font(&doc, b"T4"), "the page no longer lists the font the soft mask selects");
+}
+
 /// The same group, its content behind a predictor whose `/DecodeParms` are given by reference:
 /// the page's cleanup reads it through them, and keeps the font it selects.
 #[test]
diff --git a/crates/redact/src/tests_verify.rs b/crates/redact/src/tests_verify.rs
index 136cb2b207..6e34fba352 100644
--- a/crates/redact/src/tests_verify.rs
+++ b/crates/redact/src/tests_verify.rs
@@ -897,6 +897,119 @@ fn glyphs_are_placed_with_the_text_matrix_and_the_form_matrix() {
     assert!(proof.entries[0].detail.contains("glyph(s) still show"));
 }
 
+/// The proof reads an operator's operands from the end, as the renderer does: a surplus before
+/// them doesn't hide the text a `Tf`, `TJ` or `Do` after it draws, or the image a `Do` draws.
+#[test]
+fn the_proof_reads_operands_from_the_end() {
+    let blank = marked_content(b"BT /F1 10 Tf 10 200 Td (Public) Tj ET", Spec::default());
+    let snap = Snapshot::capture(&blank, None).unwrap();
+    let form = stream(
+        "/Type /XObject /Subtype /Form /BBox [0 0 300 300] /Resources << /Font << /F1 5 0 R >> >>",
+        b"BT /F1 10 Tf 10 100 Td (SECRETVALUE) Tj ET",
+    );
+    let image = stream("/Type /XObject /Subtype /Image /Width 1 /Height 1 /ColorSpace /DeviceGray /BitsPerComponent 8", b"o");
+    let image_form =
+        stream("/Type /XObject /Subtype /Form /BBox [0 0 300 300] /Resources << /XObject << /Im1 8 0 R >> >>", b"q 50 0 0 12 10 98 cm (x) /Im1 Do Q");
+    for (content, spec) in [
+        (&b"BT (x) /F1 10 Tf 10 100 Td (SECRETVALUE) Tj ET"[..], Spec::default()),
+        // The size: text starting outside the region reaches into it only at its size.
+        (b"BT (x) /F1 10 Tf -60 100 Td (AAAAAAAAAAAAAAAAAAAAAAAAAAAA) Tj ET", Spec::default()),
+        (b"BT /F1 10 Tf 10 100 Td (x) [(SECRETVALUE)] TJ ET", Spec::default()),
+        (b"(x) /Fm1 Do", Spec { resources: "/XObject << /Fm1 7 0 R >>", extra: vec![form.clone()], ..Spec::default() }),
+        // An image under the mark, and one in a form under it.
+        (b"q 50 0 0 12 10 98 cm (x) /Im1 Do Q", Spec { resources: "/XObject << /Im1 7 0 R >>", extra: vec![image.clone()], ..Spec::default() }),
+        (b"(x) /Fm1 Do", Spec { resources: "/XObject << /Fm1 7 0 R >>", extra: vec![image_form.clone(), image.clone()], ..Spec::default() }),
+    ] {
+        let mut doc = marked_content(content, spec);
+        doc.require_full_save();
+        let proof = snap.prove(&doc, None, &ProofOptions::default());
+        assert_eq!(proof.entries[0].status, Status::Failed, "{}: {}", String::from_utf8_lossy(content), proof.to_text());
+    }
+}
+
+/// The proof reads the text state's operands from the end too. In each case the text starts outside
+/// the region and only the operand after the surplus brings a glyph into it: char spacing, word
+/// spacing, horizontal scaling, leading with `T*`, rise, and the spacing `"` sets.
+#[test]
+fn the_proof_reads_the_text_states_operands_from_the_end() {
+    let blank = marked_content(b"BT /F1 10 Tf 10 200 Td (Public) Tj ET", Spec::default());
+    let snap = Snapshot::capture(&blank, None).unwrap();
+    for content in [
+        &b"BT /F1 10 Tf -60 100 Td (x) 70 Tc (AB) Tj ET"[..],
+        b"BT /F1 10 Tf -60 100 Td (x) 70 Tw (A B) Tj ET",
+        b"BT /F1 10 Tf -60 100 Td (x) 1500 Tz (AB) Tj ET",
+        b"BT /F1 10 Tf 10 200 Td (x) 100 TL T* (A) Tj ET",
+        b"BT /F1 10 Tf 10 200 Td (x) -100 Ts (A) Tj ET",
+        b"BT /F1 10 Tf -60 100 Td (x) 0 70 (AB) \" ET",
+    ] {
+        let mut doc = marked_content(content, Spec::default());
+        doc.require_full_save();
+        let proof = snap.prove(&doc, None, &ProofOptions::default());
+        assert_eq!(proof.entries[0].status, Status::Failed, "{}: {}", String::from_utf8_lossy(content), proof.to_text());
+    }
+}
+
+/// The proof reads a path's points from the end too: a square under the region, its points after
+/// a surplus number, still paints there.
+#[test]
+fn the_proof_reads_a_paths_points_from_the_end() {
+    let blank = marked_content(b"BT /F1 10 Tf 10 200 Td (Public) Tj ET", Spec::default());
+    let snap = Snapshot::capture(&blank, None).unwrap();
+    for content in [
+        &b"0 0 1 rg 9 20 98 m 9 60 98 l 9 60 108 l 9 20 108 l h f"[..],
+        b"0 0 1 rg 9 20 98 40 10 re f",
+        // Curves from a point outside the region whose own points reach into it.
+        b"0 0 1 rg 9 200 200 m 9 20 98 40 100 60 108 c h f",
+        b"0 0 1 rg 9 200 200 m 9 20 98 60 108 v h f",
+        b"0 0 1 rg 9 200 200 m 9 20 98 60 108 y h f",
+        // A segment after a surplus, from a point outside the region.
+        b"0 0 1 rg 200 200 m 200 20 100 l h f",
+        b"0 0 1 rg 200 200 m 200 20 100 30 100 40 100 c h f",
+        b"0 0 1 rg 200 200 m 200 20 100 40 100 v h f",
+        b"0 0 1 rg 200 200 m 200 20 100 40 100 y h f",
+    ] {
+        let mut doc = marked_content(content, Spec::default());
+        doc.require_full_save();
+        let proof = snap.prove(&doc, None, &ProofOptions::default());
+        assert_eq!(proof.entries[0].status, Status::Failed, "{}: {}", String::from_utf8_lossy(content), proof.to_text());
+    }
+}
+
+/// Which font a `Tf` selects, and which strings a `TJ` shows, are read from the end too: text an
+/// undecodable font shows after a surplus operand, away from the mark, leaves the region
+/// unverifiable. Read from the front, no font was set, or no string was shown, and it passed.
+#[test]
+fn the_proof_reads_the_font_and_the_strings_from_the_end() {
+    for content in [&b"BT (x) /F2 10 Tf 10 200 Td <00410042> Tj ET"[..], b"BT /F2 10 Tf 10 200 Td (x) [<00410042>] TJ ET"] {
+        let mut doc = open(build_with(content, opaque_spec()));
+        mark(&mut doc, &[[150.0, 20.0, 200.0, 40.0]]);
+        let (_, proof) = run(&mut doc);
+        assert_eq!(proof.entries[0].status, Status::Unverifiable, "{}: {}", String::from_utf8_lossy(content), proof.to_text());
+    }
+}
+
+/// An image a Type 3 glyph (one without resources of its own, drawing through the page's) draws
+/// after a surplus operand can't be placed, as one it draws without one can't: the region is
+/// unverifiable.
+#[test]
+fn an_image_a_type3_glyph_draws_after_a_surplus_operand_is_found() {
+    let spec = Spec {
+        resources: "/Font << /F1 5 0 R /T3 7 0 R >> /XObject << /Im0 9 0 R >>",
+        extra: vec![
+            b"<< /Type /Font /Subtype /Type3 /FontBBox [0 0 10 10] /FontMatrix [0.1 0 0 0.1 0 0] /CharProcs << /a 8 0 R >> \
+               /Encoding << /Differences [97 /a] >> /FirstChar 97 /LastChar 97 /Widths [10] >>"
+                .to_vec(),
+            stream("", b"10 0 d0 (x) /Im0 Do"),
+            stream("/Type /XObject /Subtype /Image /Width 1 /Height 1 /ColorSpace /DeviceGray /BitsPerComponent 8", b"o"),
+        ],
+        ..Spec::default()
+    };
+    let mut doc = open(build_with(b"BT /F1 10 Tf 10 100 Td (SECRETVALUE) Tj ET BT /T3 12 Tf 150 20 Td (a) Tj ET", spec));
+    mark(&mut doc, &[REGION]);
+    let (_, proof) = run(&mut doc);
+    assert_eq!(proof.entries[0].status, Status::Unverifiable, "{}", proof.to_text());
+}
+
 #[test]
 fn an_ambiguous_needle_is_still_swept_outside_page_content() {
     // The word also stays on the page legitimately (so page text, the raw file and decoded
diff --git a/crates/redact/src/type3.rs b/crates/redact/src/type3.rs
index 8f8579a7f4..11d5a76f6a 100644
--- a/crates/redact/src/type3.rs
+++ b/crates/redact/src/type3.rs
@@ -151,7 +151,7 @@ fn record_used(op: &pdfcraft_content::Op, used: &mut UsedInGlyphs) {
                 }
             }
             b"cs" | b"CS" => {
-                if let Some(n) = op.name(0) {
+                if let Some(n) = op.last_name() {
                     used.colorspaces.insert(n.to_vec());
                 }
             }
@@ -166,17 +166,17 @@ fn record_used(op: &pdfcraft_content::Op, used: &mut UsedInGlyphs) {
                 }
             }
             b"gs" => {
-                if let Some(n) = op.name(0) {
+                if let Some(n) = op.last_name() {
                     used.extgstates.insert(n.to_vec());
                 }
             }
             b"Tf" => {
-                if let Some(n) = op.name(0) {
+                if let Some(n) = op.name_back(1) {
                     used.fonts.insert(n.to_vec());
                 }
             }
             b"BDC" | b"DP" => {
-                if let Some(n) = op.name(1) {
+                if let Some(n) = op.last_name() {
                     used.properties.insert(n.to_vec());
                 }
             }
@@ -315,7 +315,7 @@ fn scan_content_stream(
             }
             b"gs" => {
                 apply_text_op(ctx, res, &op, &mut current_font);
-                if let Some(name) = op.name(0) {
+                if let Some(name) = op.last_name() {
                     scan_soft_mask(ctx, res, holder_ref, name, depth)?;
                 }
             }
@@ -338,12 +338,12 @@ fn scan_content_stream(
 fn apply_text_op(ctx: &mut ScanContext<'_>, res: &Dict, op: &pdfcraft_content::Op, current_font: &mut Option<FontKey>) {
     match op.op.as_slice() {
         b"Tf" => {
-            if let Some(name) = op.name(0) {
+            if let Some(name) = op.name_back(1) {
                 *current_font = resolve_font_in_res(ctx.doc, res, name).map(|(k, _)| k);
             }
         }
         b"gs" => {
-            if let Some(name) = op.name(0)
+            if let Some(name) = op.last_name()
                 && let Some((k, _)) = resolve_extgstate_font(ctx.doc, res, name)
             {
                 *current_font = Some(k);
@@ -477,7 +477,7 @@ fn add_soft_mask_ops(doc: &Document, res: &Dict, ops: &mut Vec<pdfcraft_content:
     while let Some(op) = ops.get(cursor) {
         let selected = match op.op.as_slice() {
             b"gs" => op
-                .name(0)
+                .last_name()
                 .and_then(|n| states.get(n))
                 .and_then(|s| doc.resolve(s).as_dict().and_then(|s| s.get(b"SMask").cloned()))
                 .and_then(|m| doc.resolve(&m).as_dict().and_then(|m| m.get(b"G").and_then(Object::as_ref))),
@@ -601,11 +601,11 @@ pub(crate) fn prune_type3_from_resources(
     let mut drawn_font_names = HashSet::new();
     for op in &ops {
         if op.is("Tf") {
-            if let Some(name) = op.name(0) {
+            if let Some(name) = op.name_back(1) {
                 drawn_font_names.insert(name.to_vec());
             }
         } else if op.is("gs")
-            && let Some(name) = op.name(0)
+            && let Some(name) = op.last_name()
         {
             let extg = res_dict(doc, res, b"ExtGState");
             if let Some(font_obj) = extg.get(name).and_then(|state_obj| gs_font_object(doc, state_obj)) {
diff --git a/crates/redact/src/verify/extract.rs b/crates/redact/src/verify/extract.rs
index 63dbeff342..4c76cc6131 100644
--- a/crates/redact/src/verify/extract.rs
+++ b/crates/redact/src/verify/extract.rs
@@ -16,7 +16,7 @@ pub(super) fn carries_glyphs(op: &pdfcraft_content::Op) -> bool {
     let nonempty = |o: &Object| o.as_string().is_some_and(|s| !s.bytes.is_empty());
     match op.op.as_slice() {
         b"Tj" | b"'" | b"\"" => op.operands.last().is_some_and(nonempty),
-        b"TJ" => op.operands.first().and_then(Object::as_array).is_some_and(|a| a.iter().any(nonempty)),
+        b"TJ" => op.back(0).and_then(Object::as_array).is_some_and(|a| a.iter().any(nonempty)),
         _ => false,
     }
 }
@@ -573,7 +573,7 @@ impl Extractor<'_> {
         let o = op.op.as_slice();
         // Strings and TJ adjustments, in order.
         let items: Vec<&Object> = match o {
-            b"TJ" => op.operands.first().and_then(Object::as_array).map(|a| a.iter().collect()).unwrap_or_default(),
+            b"TJ" => op.back(0).and_then(Object::as_array).map(|a| a.iter().collect()).unwrap_or_default(),
             _ => op.operands.last().into_iter().collect(),
         };
         let mut any_text = false;
@@ -658,14 +658,15 @@ impl Extractor<'_> {
                     tm = Matrix::IDENTITY;
                     tlm = Matrix::IDENTITY;
                 }
-                b"Tc" => gs.tc = op.num(0).unwrap_or(0.0),
-                b"Tw" => gs.tw = op.num(0).unwrap_or(0.0),
-                b"Tz" => gs.th = op.num(0).unwrap_or(100.0) / 100.0,
-                b"TL" => gs.tl = op.num(0).unwrap_or(0.0),
-                b"Ts" => gs.rise = op.num(0).unwrap_or(0.0),
+                // Operands are read from the end, as the renderer reads them.
+                b"Tc" => gs.tc = op.num_back(0).unwrap_or(0.0),
+                b"Tw" => gs.tw = op.num_back(0).unwrap_or(0.0),
+                b"Tz" => gs.th = op.num_back(0).unwrap_or(100.0) / 100.0,
+                b"TL" => gs.tl = op.num_back(0).unwrap_or(0.0),
+                b"Ts" => gs.rise = op.num_back(0).unwrap_or(0.0),
                 b"Tf" => {
-                    gs.font = op.name(0).map(<[u8]>::to_vec).unwrap_or_default();
-                    gs.size = op.num(1).unwrap_or(0.0);
+                    gs.font = op.name_back(1).map(<[u8]>::to_vec).unwrap_or_default();
+                    gs.size = op.num_back(0).unwrap_or(0.0);
                 }
                 b"Td" | b"TD" => {
                     if let Some([x, y]) = op.nums::<2>() {
@@ -692,7 +693,7 @@ impl Extractor<'_> {
                         tm = tlm;
                     }
                     if o == b"\""
-                        && let (Some(aw), Some(ac)) = (op.num(0), op.num(1))
+                        && let (Some(aw), Some(ac)) = (op.num_back(2), op.num_back(1))
                     {
                         (gs.tw, gs.tc) = (aw, ac);
                     }
@@ -707,7 +708,7 @@ impl Extractor<'_> {
                     self.show_text(font, &op, &gs, &mut tm, placed);
                 }
                 b"Do" => {
-                    let Some(name) = op.name(0) else { continue };
+                    let Some(name) = op.last_name() else { continue };
                     let Some(entry) = xobjects.get(name) else { continue };
                     if let Object::Stream(s) = &*doc.resolve(entry)
                         && s.dict.name(b"Subtype") == Some(b"Form")
diff --git a/crates/redact/src/verify/geometry.rs b/crates/redact/src/verify/geometry.rs
index 7ea0de5699..7b6833edef 100644
--- a/crates/redact/src/verify/geometry.rs
+++ b/crates/redact/src/verify/geometry.rs
@@ -188,7 +188,7 @@ impl Geo<'_> {
                     }
                 }
                 b"Do" => {
-                    let Some(entry) = op.name(0).and_then(|n| xobjects.get(n)) else { continue };
+                    let Some(entry) = op.last_name().and_then(|n| xobjects.get(n)) else { continue };
                     let obj = self.doc.resolve(entry);
                     let Object::Stream(s) = &*obj else { continue };
                     match s.dict.name(b"Subtype") {
@@ -344,7 +344,7 @@ impl Geo<'_> {
             match op.op.as_slice() {
                 b"BI" => return Ok(true),
                 b"Do" => {
-                    let Some(entry) = op.name(0).and_then(|n| xobjects.get(n)) else { continue };
+                    let Some(entry) = op.last_name().and_then(|n| xobjects.get(n)) else { continue };
                     let Object::Stream(x) = &*self.doc.resolve(entry) else { continue };
                     match x.dict.name(b"Subtype") {
                         Some(b"Image") => return Ok(true),
@@ -372,21 +372,28 @@ impl Geo<'_> {
 /// carries) by one construction operator.
 fn extend_path(op: &pdfcraft_content::Op, ctm: &Matrix, sub: &mut Vec<Vec<(f64, f64)>>, clip: &mut Option<bool>) {
     let o = op.op.as_slice();
-    let nums: Vec<f64> = op.operands.iter().filter_map(Object::as_f64).collect();
     let at = |x: f64, y: f64| ctm.apply(x, y);
+    // Each takes its numbers from the end, as the renderer reads them: a surplus before them is
+    // ignored, not read as a point.
+    let points: Option<Vec<(f64, f64)>> = match o {
+        b"l" => op.nums::<2>().map(|[x, y]| vec![at(x, y)]),
+        b"c" => op.nums::<6>().map(|[x1, y1, x2, y2, x3, y3]| vec![at(x1, y1), at(x2, y2), at(x3, y3)]),
+        b"v" | b"y" => op.nums::<4>().map(|[x1, y1, x2, y2]| vec![at(x1, y1), at(x2, y2)]),
+        _ => None,
+    };
     match o {
         b"m" => {
-            if let [x, y] = nums[..] {
+            if let Some([x, y]) = op.nums::<2>() {
                 sub.push(vec![at(x, y)]);
             }
         }
         b"l" | b"c" | b"v" | b"y" => {
-            if let Some(cur) = sub.last_mut() {
-                cur.extend(nums.as_chunks::<2>().0.iter().map(|p| at(p[0], p[1])));
+            if let (Some(cur), Some(points)) = (sub.last_mut(), points) {
+                cur.extend(points);
             }
         }
         b"re" => {
-            if let [x, y, w, h] = nums[..] {
+            if let Some([x, y, w, h]) = op.nums::<4>() {
                 sub.push(vec![at(x, y), at(x + w, y), at(x + w, y + h), at(x, y + h)]);
             }
         }
diff --git a/crates/redact/tests/operator_work.rs b/crates/redact/tests/operator_work.rs
new file mode 100644
index 0000000000..e4340fc021
--- /dev/null
+++ b/crates/redact/tests/operator_work.rs
@@ -0,0 +1,98 @@
+//! Work regressions for what a redaction looks up at operators a stream can hold thousands of: the
+//! tags cleanup's named property lists at each `BDC` are not read whole each time. A test binary of
+//! its own, so that none of the crate's other tests shares its process, and its tests run one at a
+//! time. Each test compares two timings of its own, the least of three runs each, with many
+//! entries or operators and with one, not a fixed time. The bound leaves room for slower machines:
+//! each regression took seconds against milliseconds.
+
+use std::sync::{Arc, Mutex, PoisonError};
+use std::time::{Duration, Instant};
+
+use pdfcraft_annot::{Meta, NewAnnotation, Shape, Style, add_annotation, rect_quad};
+use pdfcraft_cos::Document;
+use pdfcraft_redact::apply;
+use pdfcraft_testkit::{Pdf, stream_obj};
+
+/// One page with `resources` and `extra` objects (from object 5 on), drawing a word under a mark
+/// (so the redaction rewrites the page) and then `ops`.
+fn page(resources: &str, ops: &[u8], extra: Vec<Vec<u8>>) -> Document {
+    let content = [b"BT /F1 10 Tf 20 260 Td (SECRET) Tj ET ".as_slice(), ops].concat();
+    let mut objs = vec![
+        b"<< /Type /Catalog /Pages 2 0 R >>".to_vec(),
+        b"<< /Type /Pages /Kids [3 0 R] /Count 1 >>".to_vec(),
+        format!(
+            "<< /Type /Page /Parent 2 0 R /MediaBox [0 0 300 300] /Contents 4 0 R /Resources << /Font << /F1 << /Type /Font /Subtype /Type1 /BaseFont /Helvetica >> >> {resources} >> >>"
+        )
+        .into_bytes(),
+        stream_obj("", content),
+    ];
+    objs.extend(extra);
+    let mut doc = Document::open(Arc::new(Pdf::new().objs(objs).build())).unwrap();
+    let shape = Shape::Redact { quads: vec![rect_quad([0.0, 200.0, 300.0, 300.0])], overlay: String::new(), look: Default::default() };
+    let style = Style::default_for(&shape);
+    add_annotation(&mut doc, &NewAnnotation { page: 0, shape, style, contents: String::new(), author: "Synthetic test".into() }, &Meta::default())
+        .unwrap();
+    doc
+}
+
+/// One page whose `/Properties` holds `entries` entries, drawing `ops`.
+fn properties(entries: usize, ops: &[u8]) -> Document {
+    let lists: String = (0..entries).map(|i| format!("/M{i} << /Lang (en) >> ")).collect();
+    page(&format!("/Properties << {lists}>>"), ops, Vec::new())
+}
+
+/// One page whose property list `/M0` is object 5, which gives its `MCID` as object 6 and holds
+/// 400,000 more entries: larger than the document keeps, so that reading it again parses it again,
+/// all of it, once another object has been read since. The page draws `ops`.
+fn oversized(ops: &[u8]) -> Document {
+    let more: String = (0..400_000).map(|i| format!("/J{i} /DeviceGray ")).collect();
+    page("/Properties << /M0 5 0 R >>", ops, vec![format!("<< /MCID 6 0 R {more}>>").into_bytes(), b"0".to_vec()])
+}
+
+/// The tests' lock: they run one at a time, so that none is timed while another works.
+static SERIAL: Mutex<()> = Mutex::new(());
+
+fn one_at_a_time() -> std::sync::MutexGuard<'static, ()> {
+    SERIAL.lock().unwrap_or_else(PoisonError::into_inner)
+}
+
+/// How long redacting a document `make` builds takes, the least of three runs.
+fn redaction(make: impl Fn() -> Document) -> Duration {
+    (0..3)
+        .map(|_| {
+            let mut doc = make();
+            let start = Instant::now();
+            let report = apply(&mut doc, None).unwrap();
+            let took = start.elapsed();
+            assert_eq!(report.glyphs, 6, "the word under the mark goes");
+            took
+        })
+        .min()
+        .unwrap_or_default()
+}
+
+/// Whether `many` took about as long as `one`.
+fn about_as_long(many: Duration, one: Duration) -> bool {
+    many < one * 10 + Duration::from_secs(1)
+}
+
+/// Written when the tags cleanup resolved the page's `/Properties` at every named `BDC`: 20,000 of
+/// them with 5,000 entries took 28 s against 0.07 s with one entry (optimized). Each `BDC` here
+/// names another entry, so that it is the lists, not each name's answer, that are read once.
+#[test]
+fn named_property_lists_are_read_once_for_a_page() {
+    let _serial = one_at_a_time();
+    let ops: Vec<u8> = (0..5_000).map(|i| format!("/P /M{i} BDC EMC ")).collect::<String>().into_bytes();
+    let (one, many) = (redaction(|| properties(1, &ops)), redaction(|| properties(5_000, &ops)));
+    assert!(about_as_long(many, one), "5,000 entries {many:?}, one {one:?}");
+}
+
+/// Written when the tags cleanup read a named property list's `MCID` by reference at each `BDC`: a
+/// list larger than the document keeps was parsed again at each, 50 of them taking 12.3 s against
+/// 0.44 s with the `MCID` given directly (optimized).
+#[test]
+fn an_oversized_property_list_is_read_once_for_a_stream() {
+    let _serial = one_at_a_time();
+    let (one, many) = (redaction(|| oversized(b"/P /M0 BDC EMC ")), redaction(|| oversized(&b"/P /M0 BDC EMC ".repeat(100))));
+    assert!(about_as_long(many, one), "100 operators {many:?}, one {one:?}");
+}