diff --git a/crates/model/src/extrude.rs b/crates/model/src/extrude.rs
index 4cf575f28..f7afdabe6 100644
--- a/crates/model/src/extrude.rs
+++ b/crates/model/src/extrude.rs
@@ -130,24 +130,21 @@ pub fn group_contours(contours: Vec<Vec<P>>) -> Vec<Outline> {
         .iter()
         .map(|c| c.iter().fold([[f64::MAX; 2], [f64::MIN; 2]], |[lo, hi], p| [[lo[0].min(p[0]), lo[1].min(p[1])], [hi[0].max(p[0]), hi[1].max(p[1])]]))
         .collect();
-    // The innermost container of each contour: the smallest larger contour holding a vertex of
-    // it (nested contours do not cross); its bounding box must hold the vertex first.
-    let parent: Vec<Option<usize>> = (0..n)
-        .map(|i| {
-            let p = cs[i][0];
-            (0..n)
-                .filter(|&j| j != i && area[j] > area[i])
-                .filter(|&j| (bounds[j][0][0]..=bounds[j][1][0]).contains(&p[0]) && (bounds[j][0][1]..=bounds[j][1][1]).contains(&p[1]))
-                .filter(|&j| point_in(p, &cs[j]))
-                .min_by(|&a, &b| area[a].total_cmp(&area[b]))
-        })
-        .collect();
-    // Nesting depth, containers (the larger contours) first.
-    let mut by_area: Vec<usize> = (0..n).collect();
-    by_area.sort_by(|&a, &b| area[b].total_cmp(&area[a]));
+    // The containers of each contour: the larger contours holding a vertex of it (nested contours
+    // do not cross); the bounding box must hold the vertex first. Depth is their count, so
+    // overlapping (non-nested) paths keep every container they sit inside; the innermost
+    // container (smallest area) takes a hole.
+    let mut parent: Vec<Option<usize>> = vec![None; n];
     let mut depth = vec![0usize; n];
-    for &i in &by_area {
-        depth[i] = parent[i].map_or(0, |p| depth[p] + 1);
+    for i in 0..n {
+        let p = cs[i][0];
+        let containers: Vec<usize> = (0..n)
+            .filter(|&j| j != i && area[j] > area[i])
+            .filter(|&j| (bounds[j][0][0]..=bounds[j][1][0]).contains(&p[0]) && (bounds[j][0][1]..=bounds[j][1][1]).contains(&p[1]))
+            .filter(|&j| point_in(p, &cs[j]))
+            .collect();
+        depth[i] = containers.len();
+        parent[i] = containers.into_iter().min_by(|&a, &b| area[a].total_cmp(&area[b]));
     }
     let mut outlines: Vec<Outline> = vec![];
     let mut slot = vec![usize::MAX; n];
diff --git a/crates/model/src/fbx.rs b/crates/model/src/fbx.rs
index bca387ff2..c6f6c9523 100644
--- a/crates/model/src/fbx.rs
+++ b/crates/model/src/fbx.rs
@@ -851,6 +851,8 @@ fn parse_within(bytes: &[u8], resolve: &dyn Fn(&str) -> Option<Vec<u8>>, limit:
     let mut textures: Vec<Arc<Texture>> = vec![];
     let mut material_of: HashMap<i64, usize> = HashMap::new();
     let mut texture_of: HashMap<i64, Option<usize>> = HashMap::new();
+    // One pixel budget for every texture of the import.
+    let mut pixels_left = crate::MAX_IMPORT_TEXTURE_PIXELS;
     let mut load_texture = |tid: i64, textures: &mut Vec<Arc<Texture>>| -> Option<usize> {
         if let Some(t) = texture_of.get(&tid) {
             return *t;
@@ -874,7 +876,7 @@ fn parse_within(bytes: &[u8], resolve: &dyn Fn(&str) -> Option<Vec<u8>>, limit:
                     resolve(&f).or_else(|| resolve(f.rsplit('/').next()?))
                 })
             })?;
-            let t = Texture::decode(&bytes).ok()?;
+            let t = Texture::decode_within(&bytes, &mut pixels_left).ok()?;
             textures.push(Arc::new(t));
             Some(textures.len() - 1)
         })();
diff --git a/crates/model/src/gltf.rs b/crates/model/src/gltf.rs
index c614ae7f8..63a4a0076 100644
--- a/crates/model/src/gltf.rs
+++ b/crates/model/src/gltf.rs
@@ -400,10 +400,27 @@ pub(crate) fn parse_with_budget(bytes: &[u8], resolve: &dyn Fn(&str) -> Option<V
         let ws = samp.and_then(|s| s.get("wrapS")).and_then(Value::as_u64).unwrap_or(10497);
         let wt = samp.and_then(|s| s.get("wrapT")).and_then(Value::as_u64).unwrap_or(10497);
         let w = [wrap(ws), wrap(wt)];
-        let i = *texture_of.entry((src, w)).or_insert_with(|| {
-            textures.push(if img.wrap == w { img } else { Arc::new(Texture { wrap: w, ..(*img).clone() }) });
-            textures.len() - 1
-        });
+        let i = match texture_of.get(&(src, w)) {
+            Some(&i) => i,
+            None => {
+                let tex = if img.wrap == w {
+                    img
+                } else {
+                    // A wrap variant copies the pixels, so it is charged to the import budget too;
+                    // one that does not fit is left out like an undecodable image.
+                    let cost = u64::from(img.width) * u64::from(img.height);
+                    if cost > pixels_left {
+                        tex_map.push(None);
+                        continue;
+                    }
+                    pixels_left -= cost;
+                    Arc::new(Texture { wrap: w, ..(*img).clone() })
+                };
+                textures.push(tex);
+                texture_of.insert((src, w), textures.len() - 1);
+                textures.len() - 1
+            }
+        };
         tex_map.push(Some(i));
     }
     let tref = |v: Option<&Value>| -> Option<TexRef> {
diff --git a/crates/model/src/tests.rs b/crates/model/src/tests.rs
index 843a9db9e..a57ea7e9a 100644
--- a/crates/model/src/tests.rs
+++ b/crates/model/src/tests.rs
@@ -432,6 +432,16 @@ fn contours_group_into_outlines_by_nesting() {
     assert_eq!(g.iter().map(|o| o.holes.len()).sum::<usize>(), 2);
 }
 
+#[test]
+fn overlapping_contours_keep_every_container_in_their_depth() {
+    let rect = |x0: f64, y0: f64, x1: f64, y1: f64| vec![[x0, y0], [x1, y0], [x1, y1], [x0, y1]];
+    // C's first vertex lies inside both A and B, which overlap without nesting: C is two deep,
+    // an outer contour, not a hole cut out of B.
+    let g = group_contours(vec![rect(0.0, 0.0, 10.0, 10.0), rect(5.0, -2.0, 13.0, 8.0), rect(9.0, 1.0, 12.0, 2.0)]);
+    assert_eq!(g.len(), 3);
+    assert_eq!(g.iter().map(|o| o.holes.len()).sum::<usize>(), 0);
+}
+
 #[test]
 fn gltf_cameras_and_punctual_lights() {
     let doc = r#"{