diff --git a/crates/optimize/src/images.rs b/crates/optimize/src/images.rs
index 1a9a918ac8..ef65634d07 100644
--- a/crates/optimize/src/images.rs
+++ b/crates/optimize/src/images.rs
@@ -286,21 +286,31 @@ fn color_transform(doc: &Document, s: &Stream) -> Option<Option<i64>> {
     }
 }
 
+/// Markers and fill bytes [`adobe_transform`] reads before the first scan, at most. Encoders
+/// write a few dozen segments.
+const MAX_HEADER_STEPS: usize = 4096;
+
 /// The transform flag of a JPEG's Adobe APP14 segment (0: samples stored as they are,
 /// 1: YCbCr, 2: YCCK), the last one if there are several, as decoders read them; `Some(None)`
-/// without one. `None` if the segments before the first scan can't be read.
+/// without one. `None` if the segments before the first scan can't be read, which includes a
+/// stray byte between segments and a header of more than [`MAX_HEADER_STEPS`] steps.
+///
+/// Each step reads one marker or fill byte and jumps over its segment, so the work is bounded
+/// by the step count, not by the size of the stream. That matters: Optimize asks again for every
+/// group of fragments it tries, and the same image can be drawn many times.
 fn adobe_transform(data: &[u8]) -> Option<Option<u8>> {
     if data.get(..2)? != [0xFF, 0xD8] {
         return None;
     }
     let mut flag = None;
     let mut i = 2usize;
-    // Every step moves on by at least one byte, and reading past the end returns.
-    loop {
+    // Reading past the end returns.
+    for _ in 0..MAX_HEADER_STEPS {
+        // Decoders skip stray bytes between segments, but a stream can hold megabytes of them
+        // and each would be a step: the header counts as unreadable and the image is left as
+        // it is.
         if *data.get(i)? != 0xFF {
-            // Stray bytes between segments, which decoders skip.
-            i = i.checked_add(1)?;
-            continue;
+            return None;
         }
         let marker = *data.get(i.checked_add(1)?)?;
         match marker {
@@ -325,6 +335,7 @@ fn adobe_transform(data: &[u8]) -> Option<Option<u8>> {
             }
         }
     }
+    None
 }
 
 /// 8-bit samples of a JPEG `w` × `h` with `n` components (grey or RGB): YCbCr converted to RGB
diff --git a/crates/optimize/tests/jpeg_color_transform.rs b/crates/optimize/tests/jpeg_color_transform.rs
index 77a3293523..a84dea1cde 100644
--- a/crates/optimize/tests/jpeg_color_transform.rs
+++ b/crates/optimize/tests/jpeg_color_transform.rs
@@ -9,7 +9,7 @@
 use std::sync::Arc;
 
 use pdfcraft_cos::{Dict, Document, ObjRef, Object, SaveOptions, Stream, write_full};
-use pdfcraft_optimize::{Settings, optimize};
+use pdfcraft_optimize::{OptimizeError, Settings, Stage, optimize, optimize_with_progress};
 
 /// A photo-like RGB picture: colourful gradients with a little texture, so the colour transform
 /// matters everywhere and a medium-quality JPEG is smaller than a maximum-quality one.
@@ -361,3 +361,55 @@ fn merging_jpeg_strips_keeps_their_colour_transform() {
     let difference = mean_difference(&before, &render(&doc, 1.0));
     assert!(difference <= TOLERANCE, "colours moved by {difference:.1}");
 }
+
+/// `jpeg` with `bytes` right after its SOI marker.
+fn after_soi(jpeg: &[u8], bytes: &[u8]) -> Vec<u8> {
+    let mut v = jpeg[..2].to_vec();
+    v.extend_from_slice(bytes);
+    v.extend_from_slice(&jpeg[2..]);
+    v
+}
+
+#[test]
+fn a_jpeg_header_that_takes_more_than_a_few_steps_to_read_is_left_as_it_is() {
+    // Decoders skip stray bytes between segments and any number of fill bytes before a marker,
+    // so a stream can make a header scan walk megabytes. Optimize reads the header again for
+    // every group of fragments it tries: it stops at the first stray byte, or after a few
+    // thousand steps, and leaves such an image as it is.
+    let (w, h) = (128, 128);
+    let plain = rgb_jpeg(&photo(w, h), w, h);
+    for (what, jpeg, expect) in [
+        ("three fill bytes before the first segment", after_soi(&plain, &[0xFF; 3]), Outcome::Reencoded),
+        ("one stray byte before the first segment", after_soi(&plain, &[0]), Outcome::Untouched),
+        ("8 MB of stray bytes before the first segment", after_soi(&plain, &vec![0; 8_000_000]), Outcome::Untouched),
+        ("10,000 fill bytes before the first segment", after_soi(&plain, &[0xFF; 10_000]), Outcome::Untouched),
+    ] {
+        let (mut doc, img) = showing(w, h, 72, "DeviceRGB", jpeg, Parms::None);
+        let original = stream(&doc, img);
+        optimize(&mut doc, &Settings::default()).unwrap();
+        let outcome = if stream(&doc, img) == original { Outcome::Untouched } else { Outcome::Reencoded };
+        assert_eq!(outcome, expect, "{what}");
+    }
+}
+
+#[test]
+fn cancelling_works_from_the_first_call_with_a_jpeg_drawn_many_times() {
+    // One JPEG with 8 MB of stray bytes after SOI, drawn 64 times at the same place (the case
+    // reported on #3012). Fragment merging reads its header for each group it tries, before the
+    // first progress call. The header scan stops at the first stray byte, so that call is the
+    // first image, and cancelling there stops Optimize.
+    let (w, h) = (128, 8);
+    let jpeg = after_soi(&rgb_jpeg(&photo(w, h), w, h), &vec![0; 8_000_000]);
+    let mut doc = Document::new_empty();
+    let img = jpeg_image(&mut doc, w, h, "DeviceRGB", jpeg, Parms::None);
+    let content = format!("q {w} 0 0 {h} 0 0 cm /Im Do Q
+").repeat(64);
+    one_page(&mut doc, w, h, &[("Im".to_string(), img)], &content);
+    let mut stages = Vec::new();
+    let result = optimize_with_progress(&mut doc, &Settings::default(), &mut |stage| {
+        stages.push(stage);
+        false
+    });
+    assert!(matches!(result, Err(OptimizeError::Cancelled)), "{result:?}");
+    assert_eq!(stages, [Stage::Images { done: 0, total: 1 }]);
+}