diff --git a/crates/effects/src/distort.rs b/crates/effects/src/distort.rs
index 3fb10a925..fe3bcdd65 100644
--- a/crates/effects/src/distort.rs
+++ b/crates/effects/src/distort.rs
@@ -112,6 +112,11 @@ const MAX_REACH: f64 = 1.0e9;
 /// a 2000-anchor path. Stacked Transform effects multiply their copies (three of 1000 copies make
 /// a thousand million of one square), so the limit is on the result, not on each effect's count.
 pub(crate) const MAX_COPY_ANCHORS: usize = 2_000_000;
+/// Most image nodes a Transform effect's copies make of an art, the originals included: 1000
+/// copies of a 2000-image art. Stacked Transform effects multiply their copies (three of 1000
+/// copies make a thousand million of one image), so the limit is on the result, not on each
+/// effect's count.
+pub(crate) const MAX_COPY_IMAGES: usize = 2_000_000;
 
 /// Transform effect: scale, rotate and reflect about reference point `reference` of the bounds
 /// (the 9-point grid, 4 = centre), then move; `copies` more times, each from the last. With
@@ -152,7 +157,8 @@ pub(crate) fn transform_within(path: &PathData, b: Rect, p: &Value, seed: u64, m
 /// The Transform effect's map and how many copies of what it is applied to it makes, for bounds
 /// `b` (the reference point lies on them), params `p` and the object's `seed` for Random: the map
 /// applies to the object itself when `copies` is 0, and once more to each of `copies` copies
-/// otherwise (see [`transform_within`], and images, which have no anchors to budget).
+/// otherwise (see [`transform_within`], and images, whose copies count nodes against
+/// [`MAX_COPY_IMAGES`]).
 pub(crate) fn transform_map(b: Rect, p: &Value, seed: u64) -> (Affine, usize) {
     let random = flag(p, "random", false);
     // The share (0..1) of value `k` applied.
diff --git a/crates/effects/src/reshape.rs b/crates/effects/src/reshape.rs
index 689223044..763f30658 100644
--- a/crates/effects/src/reshape.rs
+++ b/crates/effects/src/reshape.rs
@@ -222,10 +222,24 @@ pub(crate) fn reshape_leaves(art: &mut Node, fx: &[&Effect]) {
 /// images follow, each mapped once more than the last. Without copies the image itself takes the
 /// map, as a path does.
 fn transform_images(n: &mut Node, m: Affine, copies: usize) {
+    transform_images_within(n, m, copies, crate::distort::MAX_COPY_IMAGES)
+}
+
+/// [`transform_images`] whose copies make at most `max` image nodes of the art, the originals
+/// included: each copy adds the image once more, and a Transform after this one copies the lot
+/// again, so copies stop where the result would pass `max` (#2042).
+pub(crate) fn transform_images_within(n: &mut Node, m: Affine, copies: usize, max: usize) {
+    let mut room = max.saturating_sub(image_count(n));
+    copy_images(n, m, copies, &mut room);
+}
+
+/// The walk of [`transform_images`]: the map and its copies go to each image in document order,
+/// each copy taking one from `room` (what the art can still grow by), until the budget is full.
+fn copy_images(n: &mut Node, m: Affine, copies: usize, room: &mut usize) {
     let Some(children) = n.children_mut() else { return };
     for c in children.iter_mut() {
         if !matches!(c.kind, NodeKind::Image(_)) {
-            transform_images(Arc::make_mut(c), m, copies);
+            copy_images(Arc::make_mut(c), m, copies, room);
             continue;
         }
         let src = (**c).clone();
@@ -240,12 +254,14 @@ fn transform_images(n: &mut Node, m: Affine, copies: usize) {
             *c = Arc::new(placed(m));
             continue;
         }
+        let made = copies.min(*room);
+        *room -= made;
         // The copies become image nodes of their own, under a group with the image's id, name and
         // place in the art (as the runs an outlined text gets).
-        let mut images: Vec<Arc<Node>> = Vec::with_capacity(copies + 1);
+        let mut images: Vec<Arc<Node>> = Vec::with_capacity(made + 1);
         images.push(Arc::new(placed(Affine::IDENTITY)));
         let mut xf = Affine::IDENTITY;
-        for _ in 0..copies {
+        for _ in 0..made {
             xf *= m;
             images.push(Arc::new(placed(xf)));
         }
@@ -255,6 +271,11 @@ fn transform_images(n: &mut Node, m: Affine, copies: usize) {
     }
 }
 
+/// How many image nodes `n` holds below itself.
+fn image_count(n: &Node) -> usize {
+    n.children().into_iter().flatten().map(|c| usize::from(matches!(c.kind, NodeKind::Image(_))) + image_count(c)).sum()
+}
+
 /// `n` with type anywhere inside it outlined and live objects evaluated, so geometry effects on
 /// it reach every member.
 pub(crate) fn outlined_members(n: &Node) -> Node {
diff --git a/crates/effects/src/tests.rs b/crates/effects/src/tests.rs
index 5c7026370..30a8cab2f 100644
--- a/crates/effects/src/tests.rs
+++ b/crates/effects/src/tests.rs
@@ -234,6 +234,49 @@ fn stacked_transform_copies_stay_within_the_anchor_budget() {
     assert_eq!(run("distort.transform", p, &square()).subpaths.len(), 1001);
 }
 
+/// #2042: stacked Transform effects multiply their image copies as they do their anchors; the
+/// image nodes they make are bounded, whatever each one's count.
+#[test]
+fn stacked_transform_copies_stay_within_the_image_budget() {
+    use std::sync::Arc;
+
+    use vectorcraft_doc::{ImageObject, NodeId};
+    let id = NodeId(9);
+    let image = || {
+        Node::new(
+            id,
+            NodeKind::Image(Box::new(ImageObject {
+                key: "k".into(),
+                width: 40,
+                height: 40,
+                xf: Affine::translate((10.0, 0.0)),
+                link: None,
+                placement: Default::default(),
+            })),
+        )
+    };
+    let count = |art: &Node| {
+        let mut xs = vec![];
+        image_xs(art, &mut xs);
+        xs.len()
+    };
+    let m = Affine::translate((70.0, 0.0));
+    let mut art = Node::group(id, vec![Arc::new(image())]);
+    let mut counts = vec![];
+    for _ in 0..3 {
+        crate::reshape::transform_images_within(&mut art, m, 1000, 100);
+        counts.push(count(&art));
+    }
+    assert_eq!(counts, [100, 100, 100], "99 copies, then no room for a copy of them");
+    // Within the budget every copy is made, and the effect's own budget takes a thousand copies.
+    let mut art = Node::group(id, vec![Arc::new(image())]);
+    crate::reshape::transform_images_within(&mut art, m, 24, 100);
+    assert_eq!(count(&art), 25);
+    let mut g = Node::group(id, vec![Arc::new(image())]);
+    g.appearance.effects.push(fx("distort.transform", json!({"moveH": 70, "copies": 1000})));
+    assert_eq!(count(&evaluate_container(&g).unwrap()), 1001);
+}
+
 #[test]
 fn transform_copies_stop_before_they_overflow() {
     let out = run("distort.transform", json!({"scaleH": 100000, "scaleV": 100000, "copies": 1000}), &square());
@@ -268,14 +311,20 @@ fn transform_on_a_group_moves_and_copies_its_images() {
     xs.sort_by(f64::total_cmp);
     assert_eq!(xs, [10.0, 80.0, 150.0], "the image and its two copies, 70 pt apart");
     // Without copies the image itself takes the transform, as a path does.
-    let mut g = Node::group(id, vec![Arc::new(Node::new(id, NodeKind::Image(Box::new(ImageObject {
-        key: "k".into(),
-        width: 40,
-        height: 40,
-        xf: Affine::translate((10.0, 0.0)),
-        link: None,
-        placement: Default::default(),
-    }))))]);
+    let mut g = Node::group(
+        id,
+        vec![Arc::new(Node::new(
+            id,
+            NodeKind::Image(Box::new(ImageObject {
+                key: "k".into(),
+                width: 40,
+                height: 40,
+                xf: Affine::translate((10.0, 0.0)),
+                link: None,
+                placement: Default::default(),
+            })),
+        ))],
+    );
     g.appearance.effects.push(fx("distort.transform", json!({"scaleH": 50, "scaleV": 50, "reference": 8})));
     let art = evaluate_container(&g).unwrap();
     let mut xs = vec![];