diff --git a/crates/engine/src/interchange/vector.rs b/crates/engine/src/interchange/vector.rs
index b52517cb3..569e8e5bc 100644
--- a/crates/engine/src/interchange/vector.rs
+++ b/crates/engine/src/interchange/vector.rs
@@ -477,35 +477,51 @@ pub fn split_at_images(doc: &Doc) -> Vec<Doc> {
             })
             .sum()
     }
-    /// Keep the shapes between images `seg − 1` and `seg`; `seen` counts images passed.
-    fn prune(g: &effectcraft_svg::Group, seg: usize, seen: &mut usize) -> effectcraft_svg::Group {
-        let mut out = g.clone();
-        out.children = vec![];
+    /// `g` without its children, holding `children` instead (nothing below `g` is copied).
+    fn shell(g: &effectcraft_svg::Group, children: Vec<Node>) -> effectcraft_svg::Group {
+        effectcraft_svg::Group {
+            name: g.name.clone(),
+            transform: g.transform,
+            opacity: g.opacity,
+            children,
+            clip: g.clip.clone(),
+            blend: g.blend,
+            mask: g.mask.clone(),
+            isolated: g.isolated,
+            knockout: g.knockout,
+        }
+    }
+    /// One traversal for every segment: the pieces of `g` as (segment, group), by ascending
+    /// segment; `seen` counts images passed. Each shape is copied once, into its own segment.
+    fn split(g: &effectcraft_svg::Group, seen: &mut usize) -> Vec<(usize, effectcraft_svg::Group)> {
+        let mut by: Vec<(usize, Vec<Node>)> = vec![];
+        let mut put = |seg: usize, node: Node| match by.last_mut() {
+            Some(last) if last.0 == seg => last.1.push(node),
+            _ => by.push((seg, vec![node])),
+        };
         for c in &g.children {
             match c {
                 Node::Image(_) => *seen += 1,
-                Node::Shape(_) => {
-                    if *seen == seg {
-                        out.children.push(c.clone());
-                    }
-                }
+                Node::Shape(_) => put(*seen, c.clone()),
                 Node::Group(s) => {
-                    let p = prune(s, seg, seen);
-                    if !p.children.is_empty() {
-                        out.children.push(Node::Group(p));
+                    for (seg, part) in split(s, seen) {
+                        put(seg, Node::Group(part));
                     }
                 }
             }
         }
-        out
+        by.into_iter().map(|(seg, children)| (seg, shell(g, children))).collect()
     }
     let n = count(&doc.root);
-    (0..=n)
-        .map(|seg| {
-            let mut d = doc.clone();
-            d.root = prune(&doc.root, seg, &mut 0);
-            d
-        })
+    let mut roots: Vec<Option<effectcraft_svg::Group>> = vec![None; n + 1];
+    for (seg, part) in split(&doc.root, &mut 0) {
+        if let Some(slot) = roots.get_mut(seg) {
+            *slot = Some(part);
+        }
+    }
+    roots
+        .into_iter()
+        .map(|root| Doc { width: doc.width, height: doc.height, root: root.unwrap_or_else(|| shell(&doc.root, vec![])), skipped: doc.skipped.clone() })
         .collect()
 }
 
@@ -655,3 +671,73 @@ pub fn masks_layer(proj: &mut Project, comp: &Comp, name: &str, outlines: Vec<Sh
     }
     l
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use effectcraft_svg::{Geom, Group, Image, Shape};
+
+    fn shape(name: &str) -> Node {
+        let geom = Geom::Rect { x: 0.0, y: 0.0, w: 1.0, h: 1.0, rx: 0.0, ry: 0.0 };
+        Node::Shape(Shape {
+            name: name.into(),
+            geom,
+            transform: Affine::IDENTITY,
+            fill: None,
+            fill_opacity: 1.0,
+            fill_rule: effectcraft_svg::FillRule::NonZero,
+            stroke: None,
+            opacity: 1.0,
+        })
+    }
+    fn image() -> Node {
+        Node::Image(Image { name: "i".into(), transform: Affine::IDENTITY, width: 1, height: 1, rgba: std::sync::Arc::new(vec![0; 4]), opacity: 1.0 })
+    }
+    fn group(name: &str, children: Vec<Node>) -> Node {
+        let mut g = Group::new(name);
+        g.children = children;
+        Node::Group(g)
+    }
+    fn names(g: &Group, out: &mut Vec<String>) {
+        for c in &g.children {
+            match c {
+                Node::Shape(s) => out.push(s.name.clone()),
+                Node::Group(s) => {
+                    out.push(format!("<{}", s.name));
+                    names(s, out);
+                    out.push(format!("{}>", s.name));
+                }
+                Node::Image(_) => out.push("IMG".into()),
+            }
+        }
+    }
+
+    /// Segment `k` keeps the shapes between image `k - 1` and `k`, with the groups that hold them.
+    #[test]
+    fn split_keeps_each_segments_shapes_and_their_groups() {
+        let mut root = Group::new("root");
+        root.children = vec![
+            shape("a"),
+            image(),
+            group("g1", vec![shape("b"), image(), shape("c"), group("g2", vec![shape("d"), image(), shape("e")])]),
+            image(),
+            group("empty", vec![image()]),
+            shape("f"),
+        ];
+        let doc = Doc { width: 10.0, height: 10.0, root, skipped: vec![] };
+        let segs = split_at_images(&doc);
+        assert_eq!(segs.len(), 6);
+        let got: Vec<Vec<String>> = segs
+            .iter()
+            .map(|d| {
+                let mut v = vec![];
+                names(&d.root, &mut v);
+                v
+            })
+            .collect();
+        let want: Vec<Vec<&str>> =
+            vec![vec!["a"], vec!["<g1", "b", "g1>"], vec!["<g1", "c", "<g2", "d", "g2>", "g1>"], vec!["<g1", "<g2", "e", "g2>", "g1>"], vec![], vec!["f"]];
+        assert_eq!(got, want);
+        assert!(segs.iter().all(|d| d.root.name == "root" && d.width == 10.0));
+    }
+}