diff --git a/crates/redact/src/sanitize.rs b/crates/redact/src/sanitize.rs
index 8965f82e6c..49b7adaf38 100644
--- a/crates/redact/src/sanitize.rs
+++ b/crates/redact/src/sanitize.rs
@@ -372,29 +372,43 @@ fn once(
 }
 
 /// `o` without the entries `keep` refuses, through nested arrays (an `/Order` holds sub-lists, and
-/// `/RBGroups` holds groups), each array written by reference cleaned [`once`].
-fn filtered(doc: &mut Document, o: &Object, keep: &impl Fn(&Object) -> bool, depth: usize, cleaned: &mut Cleaned) -> Result<Object, RedactError> {
+/// `/RBGroups` holds groups), each array written by reference cleaned [`once`]. `None` when `keep`
+/// refuses `o` itself, or when `o` is a sub-list (`depth` above 0) that named a layer and names
+/// none now: it goes, with the heading that labelled it.
+fn filtered(
+    doc: &mut Document,
+    o: &Object,
+    keep: &impl Fn(&Object) -> bool,
+    depth: usize,
+    cleaned: &mut Cleaned,
+) -> Result<Option<Object>, RedactError> {
     if depth > MAX_DIRECT_DEPTH {
         return Err(RedactError::TooDeep);
     }
-    let out = once(doc, o, cleaned, |doc, o, cleaned| {
+    if !keep(o) {
+        return Ok(None);
+    }
+    once(doc, o, cleaned, |doc, o, cleaned| {
         let Object::Array(a) = o else { return Ok(Some(o.clone())) };
         let mut out = Vec::new();
-        for x in a.iter().filter(|x| keep(x)) {
-            out.push(filtered(doc, x, keep, depth + 1, cleaned)?);
+        for x in a {
+            out.extend(filtered(doc, x, keep, depth + 1, cleaned)?);
         }
-        Ok(Some(Object::Array(out)))
-    })?;
-    Ok(out.unwrap_or_else(|| Object::Array(Vec::new())))
+        // Anything but a text string (a heading) is a layer or a sub-list.
+        let names = |l: &[Object]| l.iter().any(|x| !matches!(x, Object::String(_)));
+        let emptied = depth > 0 && names(a.as_slice()) && !names(out.as_slice());
+        Ok((!emptied).then_some(Object::Array(out)))
+    })
 }
 
 /// An optional-content configuration without the layers `keep` refuses, in every list that names
-/// them: on, off, order, locked, radio-button groups and usage rules (a rule left with no layer
-/// goes). A removed layer still named in any of them would stay in the file, its name included.
+/// them: on, off, order, locked, radio-button groups and usage rules (a rule, group or sub-list left
+/// with no layer goes). A removed layer still named in any of them would stay in the file, its name
+/// included.
 fn config_without(doc: &mut Document, mut d: Dict, keep: &impl Fn(&Object) -> bool, cleaned: &mut Cleaned) -> Result<Dict, RedactError> {
     for k in [&b"ON"[..], b"OFF", b"Order", b"Locked", b"RBGroups"] {
         if let Some(v) = d.get(k).cloned() {
-            let v = filtered(doc, &v, keep, 0, cleaned)?;
+            let v = filtered(doc, &v, keep, 0, cleaned)?.unwrap_or_else(|| Object::Array(Vec::new()));
             d.set(k.to_vec(), v);
         }
     }
@@ -406,7 +420,7 @@ fn config_without(doc: &mut Document, mut d: Dict, keep: &impl Fn(&Object) -> bo
             kept.extend(once(doc, rule, cleaned, |doc, rule, cleaned| {
                 let Some(mut rule) = rule.as_dict().cloned() else { return Ok(None) };
                 if let Some(layers) = rule.get(b"OCGs").cloned() {
-                    let layers = filtered(doc, &layers, keep, 0, cleaned)?;
+                    let Some(layers) = filtered(doc, &layers, keep, 0, cleaned)? else { return Ok(None) };
                     if doc.resolve(&layers).as_array().is_some_and(Vec::is_empty) {
                         return Ok(None);
                     }
diff --git a/crates/redact/src/tests.rs b/crates/redact/src/tests.rs
index 6c5d8ae800..f28fdeb353 100644
--- a/crates/redact/src/tests.rs
+++ b/crates/redact/src/tests.rs
@@ -4235,13 +4235,14 @@ fn a_shared_layer_list_is_cleaned_once() {
 }
 
 /// A removed off layer leaves every list that names it, or its dictionary, name included, stays in
-/// the file: a sub-list of the default `/Order`, a radio-button group, a usage rule, and the
-/// alternate configurations in `/Configs`.
+/// the file: a sub-list of the default `/Order` (its heading too, once it names no layer), a
+/// radio-button group (a group left empty goes), a usage rule (one that names it directly too), and
+/// the alternate configurations in `/Configs`.
 #[test]
 fn a_removed_layer_leaves_every_configuration() {
     use crate::sanitize::{Hidden, remove_hidden};
     let mut doc = pdf(vec![
-        b"<< /Type /Catalog /Pages 2 0 R /OCProperties << /OCGs [6 0 R 7 0 R] /D << /OFF [6 0 R] /Order [7 0 R [(Group) 6 0 R]] /RBGroups [[6 0 R 7 0 R]] /AS [<< /Event /Print /OCGs [6 0 R] /Category [/Print] >>] >> /Configs [8 0 R] >> >>".to_vec(),
+        b"<< /Type /Catalog /Pages 2 0 R /OCProperties << /OCGs [6 0 R 7 0 R] /D << /OFF [6 0 R] /Order [7 0 R [(Group) 6 0 R]] /RBGroups [[6 0 R 7 0 R] [6 0 R]] /AS [<< /Event /Print /OCGs [6 0 R] /Category [/Print] >> << /Event /View /OCGs 6 0 R /Category [/View] >>] >> /Configs [8 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 >> /Properties << /L1 6 0 R >> >> >>".to_vec(),
         stream("", b"/OC /L1 BDC BT /F1 10 Tf 10 50 Td (Gone) Tj ET EMC BT /F1 10 Tf 10 100 Td (Kept) Tj ET"),
@@ -4256,4 +4257,9 @@ fn a_removed_layer_leaves_every_configuration() {
     let has = |needle: &[u8]| bytes.windows(needle.len()).any(|w| w == needle);
     assert!(has(b"(Shown layer)") && has(b"(Other view)"), "the layer that stays and the configuration stay");
     assert!(!has(b"SECRETLAYERNAME"), "the removed layer survived the save");
+    assert!(!has(b"(Group)"), "the heading of a sub-list left with no layer stayed");
+    let catalog = doc.get(doc.root().unwrap());
+    let config = catalog.as_dict().and_then(|c| c.get(b"OCProperties")).and_then(Object::as_dict).and_then(|p| p.get(b"D")).and_then(Object::as_dict);
+    let group = Object::Array(vec![Object::Ref(ObjRef::new(7, 0))]);
+    assert_eq!(config.and_then(|d| d.get(b"RBGroups")), Some(&Object::Array(vec![group])), "a radio-button group left empty stayed");
 }