diff --git a/crates/compose/src/lib.rs b/crates/compose/src/lib.rs
index f110c0ecc..e8e08dba6 100644
--- a/crates/compose/src/lib.rs
+++ b/crates/compose/src/lib.rs
@@ -3325,15 +3325,22 @@ pub fn column_rule_rects(columns: &[Rect], lines: &[Line], opts: &TextFrameOptio
             continue;
         }
         // Vertical bands of the paragraphs whose lines cross this gutter.
+        // Grouped by paragraph through an index, in first-seen order: searching the bands for
+        // each line was quadratic in the number of paragraphs.
         let mut spans: Vec<(usize, f64, f64)> = Vec::new();
+        let mut band_of: HashMap<usize, usize> = HashMap::new();
         for l in lines.iter().filter(|l| l.x0 < cx && l.x1 > cx) {
             let (t, z) = (l.baseline - l.ascent, l.baseline + l.descent);
-            match spans.iter_mut().find(|s| s.0 == l.para) {
-                Some(s) => {
+            match band_of.get(&l.para) {
+                Some(&k) => {
+                    let s = &mut spans[k];
                     s.1 = s.1.min(t);
                     s.2 = s.2.max(z);
                 }
-                None => spans.push((l.para, t, z)),
+                None => {
+                    band_of.insert(l.para, spans.len());
+                    spans.push((l.para, t, z));
+                }
             }
         }
         spans.sort_by(|p, q| p.1.total_cmp(&q.1));
diff --git a/crates/compose/src/notes.rs b/crates/compose/src/notes.rs
index 1e1c852a5..67f922637 100644
--- a/crates/compose/src/notes.rs
+++ b/crates/compose/src/notes.rs
@@ -14,7 +14,7 @@
 //! With Span Footnotes Across Columns the notes of a frame share one area across all its columns,
 //! composed at the frame's text width: every column of the frame makes room for it.
 
-use std::collections::HashMap;
+use std::collections::{HashMap, HashSet};
 use std::ops::Range;
 use std::sync::Arc;
 
@@ -146,11 +146,13 @@ impl Notes {
     }
 
     /// Footnote indices referenced by a line's glyphs.
+    /// In the order they first appear; a set keeps a line with many references linear.
     pub fn refs_in(&self, glyphs: &[Glyph]) -> Vec<usize> {
         let mut v: Vec<usize> = Vec::new();
+        let mut seen = HashSet::new();
         for g in glyphs.iter().filter(|g| g.ch == FOOTNOTE_REF && g.len > 0) {
             if let Ok(k) = self.refs.binary_search(&g.byte)
-                && !v.contains(&k)
+                && seen.insert(k)
             {
                 v.push(k);
             }
diff --git a/crates/compose/src/overlay.rs b/crates/compose/src/overlay.rs
index b09ef908e..6cd3df72f 100644
--- a/crates/compose/src/overlay.rs
+++ b/crates/compose/src/overlay.rs
@@ -2,7 +2,7 @@
 //! through or up to a delimiter) and GREP styles (every match of a pattern).
 
 use std::cell::RefCell;
-use std::collections::HashMap;
+use std::collections::{HashMap, HashSet};
 use std::ops::Range;
 
 use designcraft_doc::{GrepStyle, NestedStyle, NestedUntil};
@@ -47,7 +47,9 @@ fn with_pattern<R>(pattern: &str, f: impl FnOnce(&mut Option<Grep>) -> R) -> R {
     })
 }
 
-fn is_event(u: &NestedUntil, c: char, prev: Option<char>, next: Option<char>) -> bool {
+/// Whether `c` ends one unit of `u`. `delims` is the character set of a [`NestedUntil::Chars`]
+/// delimiter, indexed once per nested style.
+fn is_event(u: &NestedUntil, delims: &HashSet<char>, c: char, prev: Option<char>, next: Option<char>) -> bool {
     match u {
         NestedUntil::Sentences => matches!(c, '.' | '!' | '?') && next.is_none_or(char::is_whitespace),
         NestedUntil::Words => c.is_whitespace() && prev.is_some_and(|p| !p.is_whitespace()),
@@ -60,7 +62,7 @@ fn is_event(u: &NestedUntil, c: char, prev: Option<char>, next: Option<char>) ->
         NestedUntil::EnSpace => c == '\u{2002}',
         // Counted by position, not by character (see `overlays`).
         NestedUntil::Dropcap => false,
-        NestedUntil::Chars(s) => s.contains(c),
+        NestedUntil::Chars(_) => delims.contains(&c),
     }
 }
 
@@ -81,18 +83,25 @@ pub(crate) fn overlays(text: &str, range: Range<usize>, nested: &[NestedStyle],
             // Through the drop cap runs to its end; up to it (it starts the paragraph) is nothing.
             stop = if ns.through { drop_end.max(pos).min(end) } else { pos };
         } else {
+            // Streamed up to the delimiter, with one character of lookahead: copying the rest of
+            // the paragraph for every nested style multiplied its length by the number of styles.
+            let delims: HashSet<char> = match &ns.until {
+                NestedUntil::Chars(s) => s.chars().collect(),
+                _ => HashSet::new(),
+            };
             let mut count = 0;
-            let chars: Vec<(usize, char)> = text[pos..end].char_indices().map(|(i, c)| (pos + i, c)).collect();
-            for (k, &(i, c)) in chars.iter().enumerate() {
-                let prev = if k > 0 { Some(chars[k - 1].1) } else { None };
-                let next = chars.get(k + 1).map(|x| x.1);
-                if is_event(&ns.until, c, prev, next) {
+            let mut prev = None;
+            let mut chars = text[pos..end].char_indices().map(|(i, c)| (pos + i, c)).peekable();
+            while let Some((i, c)) = chars.next() {
+                let next = chars.peek().map(|x| x.1);
+                if is_event(&ns.until, &delims, c, prev, next) {
                     count += 1;
                     if count >= ns.count.max(1) {
                         stop = if ns.through { i + c.len_utf8() } else { i };
                         break;
                     }
                 }
+                prev = Some(c);
             }
         }
         if stop > pos && !ns.style.is_empty() {
@@ -161,6 +170,19 @@ mod tests {
         assert!(has_last, "the most recently used pattern is still cached");
     }
 
+    /// Nested styles that stop where they start (up to a delimiter the paragraph starts with)
+    /// read one character each, not the rest of the paragraph.
+    #[test]
+    fn nested_styles_stopping_at_once_do_not_rescan_the_paragraph() {
+        let text = format!("x{}\n", "y".repeat(200_000));
+        let delim: String = ('a'..='z').chain('A'..='Z').filter(|c| *c != 'y').collect();
+        let rule = NestedStyle { style: "S".into(), through: false, count: 1, until: NestedUntil::Chars(delim) };
+        let nested = vec![rule; 5000];
+        let t = std::time::Instant::now();
+        assert!(overlays(&text, 0..text.len(), &nested, &[], 0).is_empty(), "each style styles nothing");
+        assert!(t.elapsed().as_secs() < 5, "{:?}", t.elapsed());
+    }
+
     #[test]
     fn nested_and_grep_ranges() {
         let text = "Q: what is 42? A drop of 7 words.\n".to_string();
diff --git a/crates/compose/src/shape.rs b/crates/compose/src/shape.rs
index 078848672..4ce7247d5 100644
--- a/crates/compose/src/shape.rs
+++ b/crates/compose/src/shape.rs
@@ -385,6 +385,7 @@ fn resolve_pieces(input: &ShapeInput<'_, '_>, table: &mut StyleTable<'_>) -> (Ve
         overlays.push((range.start..drop_cap.0, s.to_string()));
     }
     // Each run, cut where nested / GREP styles start and end.
+    let bands = overlay_bands(&overlays);
     let mut segments: Vec<(usize, usize, Option<&str>, &designcraft_doc::CharFormat)> = Vec::new();
     for (rr, fmt) in story.runs() {
         let a = rr.start.max(range.start);
@@ -396,14 +397,16 @@ fn resolve_pieces(input: &ShapeInput<'_, '_>, table: &mut StyleTable<'_>) -> (Ve
             segments.push((a, b, None, fmt));
             continue;
         }
-        let mut cuts: Vec<usize> = overlays.iter().flat_map(|(r, _)| [r.start, r.end]).filter(|x| *x > a && *x < b).collect();
-        cuts.push(a);
-        cuts.push(b);
-        cuts.sort_unstable();
-        cuts.dedup();
-        for w in cuts.windows(2) {
-            let top = overlays.iter().rev().find(|(r, _)| r.start <= w[0] && w[0] < r.end).map(|(_, s)| s.as_str());
-            segments.push((w[0], w[1], top, fmt));
+        // The band holding `a`, then each following band up to `b`. Bands start at 0, so one
+        // holds `a`, and each ends where the next starts (the last one at `b`).
+        let mut k = bands.partition_point(|(at, _)| *at <= a).saturating_sub(1);
+        let mut at = a;
+        while at < b {
+            let to = bands.get(k + 1).map_or(b, |(next, _)| (*next).min(b));
+            let top = bands.get(k).and_then(|(_, top)| *top).map(|i| overlays[i].1.as_str());
+            segments.push((at, to, top, fmt));
+            at = to;
+            k += 1;
         }
     }
     // Resolve every segment, then shape runs of segments that differ only in how they are
@@ -1426,3 +1429,69 @@ fn digit_mode(p: &designcraft_doc::CharProps, arabic_context: Option<bool>) -> d
         _ => Digits::Native,
     }
 }
+
+/// The stretches between `overlays`' boundaries, as `(start, overlay on top)` sorted by start:
+/// a stretch runs to the next one's start, and the one on top is the last overlay covering it
+/// (later ones win). One sweep over the boundaries; picking the top overlay by scanning them all
+/// for each stretch was quadratic when a GREP style matched every character.
+fn overlay_bands(overlays: &[(std::ops::Range<usize>, String)]) -> Vec<(usize, Option<usize>)> {
+    let mut starts: Vec<(usize, usize)> = Vec::new();
+    let mut ends: Vec<(usize, usize)> = Vec::new();
+    for (i, (r, _)) in overlays.iter().enumerate().filter(|(_, (r, _))| r.start < r.end) {
+        starts.push((r.start, i));
+        ends.push((r.end, i));
+    }
+    starts.sort_unstable();
+    ends.sort_unstable();
+    let mut cuts: Vec<usize> = starts.iter().chain(&ends).map(|x| x.0).collect();
+    cuts.push(0);
+    cuts.sort_unstable();
+    cuts.dedup();
+    let mut active = std::collections::BTreeSet::new();
+    let (mut s, mut e) = (0, 0);
+    let mut out = Vec::with_capacity(cuts.len());
+    for at in cuts {
+        while e < ends.len() && ends[e].0 <= at {
+            active.remove(&ends[e].1);
+            e += 1;
+        }
+        while s < starts.len() && starts[s].0 <= at {
+            active.insert(starts[s].1);
+            s += 1;
+        }
+        out.push((at, active.last().copied()));
+    }
+    out
+}
+
+#[cfg(test)]
+mod tests {
+    use super::overlay_bands;
+
+    /// The band sweep picks the same top overlay as checking every overlay at each boundary.
+    #[test]
+    fn overlay_bands_match_the_last_covering_overlay() {
+        let overlays: Vec<(std::ops::Range<usize>, String)> = [(2..9, "a"), (0..4, "b"), (4..4, "empty"), (3..6, "c"), (8..12, "d"), (5..7, "e")]
+            .into_iter()
+            .map(|(r, s)| (r, s.to_string()))
+            .collect();
+        let bands = overlay_bands(&overlays);
+        for at in 0..14 {
+            let k = bands.partition_point(|(start, _)| *start <= at) - 1;
+            let want = overlays.iter().rposition(|(r, _)| r.start <= at && at < r.end);
+            assert_eq!(bands[k].1, want, "at {at}");
+        }
+    }
+
+    /// One overlay per character (a GREP style matching every character) sweeps in one pass.
+    #[test]
+    fn many_overlays_are_banded_quickly() {
+        let n = 200_000;
+        let overlays: Vec<(std::ops::Range<usize>, String)> = (0..n).map(|i| (i..i + 1, "s".to_string())).collect();
+        let t = std::time::Instant::now();
+        let bands = overlay_bands(&overlays);
+        assert_eq!(bands.len(), n + 1);
+        assert_eq!(bands[n / 2], (n / 2, Some(n / 2)));
+        assert!(t.elapsed().as_secs() < 5);
+    }
+}
diff --git a/crates/compose/src/table.rs b/crates/compose/src/table.rs
index a124b1fce..5811887ae 100644
--- a/crates/compose/src/table.rs
+++ b/crates/compose/src/table.rs
@@ -5,6 +5,7 @@
 //! cell (or its fixed height); rows that don't fit continue in the next column / frame, repeating
 //! header (and footer) rows. Rows tied together by row spans never split.
 
+use std::collections::HashMap;
 use std::sync::Arc;
 
 use designcraft_doc::{Align, Cell, CellStroke, Document, ItemId, ParaProps, RowHeightMode, Table, TextFrameOptions, VerticalJustification};
@@ -404,7 +405,13 @@ fn emit(
     out: &mut ComposedStory,
 ) {
     let nc = table.ncols();
-    let ry = |r: usize| rows.iter().find(|x| x.0 == r).map(|x| x.1);
+    // Each row's top (its first occurrence in the fragment), indexed once: looking it up per cell
+    // by scanning the rows was quadratic in a fragment's row count.
+    let mut row_top: HashMap<usize, f64> = HashMap::with_capacity(rows.len());
+    for &(r, y, _) in rows {
+        row_top.entry(r).or_insert(y);
+    }
+    let ry = |r: usize| row_top.get(&r).copied();
     let header = table.header_rows();
     let body = table.body_rows();
     let nbody = body.len();