diff --git a/crates/engine/src/tests/robustness.rs b/crates/engine/src/tests/robustness.rs
index 0afd0fbb..b020062d 100644
--- a/crates/engine/src/tests/robustness.rs
+++ b/crates/engine/src/tests/robustness.rs
@@ -180,6 +180,24 @@ fn shell_after_a_drilled_hole() {
     }
 }
 
+/// Rounding an edge that runs into an earlier round of the same radius (filleting a box's
+/// edges one at a time): the same body as picking both at once. Another radius says so.
+#[test]
+fn fillet_into_an_earlier_round() {
+    let box_ = json!({"command": "solid.box", "params": {"length": 60, "width": 40, "height": 15}});
+    let both = script(json!([box_, {"command": "solid.fillet", "params": {"edges": [[30, 0, 15], [60, 0, 7]], "radius": 2}}]));
+    let one_by_one = script(json!([
+        box_,
+        {"command": "solid.fillet", "params": {"edges": [[30, 0, 15]], "radius": 2}},
+        {"command": "solid.fillet", "params": {"edges": [[60, 0, 7]], "radius": 2}}
+    ]));
+    let (a, b) = (total_volume(&both), total_volume(&one_by_one));
+    assert!((a - b).abs() < 1e-6 * a, "{a} vs {b}");
+    let mut s = script(json!([box_, {"command": "solid.fillet", "params": {"edges": [[30, 0, 15]], "radius": 2}}]));
+    let e = s.execute("solid.fillet", &json!({"edges": [[60, 0, 7]], "radius": 3})).unwrap_err();
+    assert!(e.to_string().contains("not supported yet: an edge running into an earlier round of another radius"), "{e}");
+}
+
 /// Seeds that run clean: no failure, no invalid body, no volume going the wrong way.
 #[test]
 fn fixed_seeds_run_clean() {
diff --git a/crates/kernel/src/blend.rs b/crates/kernel/src/blend.rs
index 8472bd09..102f67d4 100644
--- a/crates/kernel/src/blend.rs
+++ b/crates/kernel/src/blend.rs
@@ -361,6 +361,15 @@ fn blend(body: &Body, edges: &[Vec3], r: f64, shape: Shape, what: &str) -> Resul
             let attempt = match guard(what, || blend_one(&solid, &edge, size, r, shape)) {
                 Ok(o) => Ok((o, vec![j])),
                 // A curved edge, or one between curved faces: roll a ball along its smooth chain.
+                // A straight edge running into an earlier round of the same radius: that round
+                // undone and both edges rounded together (they meet in a mitre, as when picked
+                // at once).
+                Err(e) if !curved_case(&solid, &edge) && e.to_string().contains("edge ends must be planar") && shape == Shape::Round => {
+                    unround_and_blend(&cur, &edge, r, what).map(|b| ((*b.solid).clone(), vec![j])).map_err(|e2| match &e2 {
+                        KernelError::Failed(m) if m.starts_with("not supported yet: an edge running into") => e2,
+                        _ => KernelError::Failed(format!("{e} ({e2})")),
+                    })
+                }
                 Err(e) if !curved_case(&solid, &edge) => Err(e),
                 Err(e) => match smooth_chain(&solid, &edge) {
                     Some(ids) => {
@@ -799,6 +808,54 @@ pub fn chamfer_sides(body: &Body, edges: &[Vec3], d1: f64, side: ChamferSide, fl
     Ok(cur)
 }
 
+thread_local! {
+    static UNROUNDING: std::cell::Cell<bool> = const { std::cell::Cell::new(false) };
+}
+
+/// Round `edge` of `cur` where an end runs into an earlier round of radius `r`: the round is
+/// deleted (its faces healed back to the sharp edge) and both edges rounded in one go.
+fn unround_and_blend(cur: &Body, edge: &mt::Edge, r: f64, what: &str) -> Result<Body> {
+    if UNROUNDING.with(|c| c.get()) {
+        return Err(unsupported("rounds meeting rounds"));
+    }
+    let size = cur.size();
+    let mesh = cur.tessellate((size * 1e-3).max(1e-3))?;
+    let info = cur.faces((size * 1e-3).max(1e-3))?;
+    let curved = |f: usize| info.get(f).is_some_and(|x| x.plane_normal.is_none());
+    let ends = [from_p3(edge.absolute_front().point()), from_p3(edge.absolute_back().point())];
+    let mut round: Option<(usize, Vec3)> = None;
+    for q in ends {
+        let near = mesh
+            .triangles
+            .iter()
+            .zip(&mesh.tri_face)
+            .filter(|(_, f)| curved(**f as usize))
+            .filter_map(|(t, f)| mesh.tri(t).map(|[x, y, z]| (q.dist((x + y + z) / 3.0), *f as usize, (x + y + z) / 3.0)))
+            .min_by(|a, b| a.0.total_cmp(&b.0));
+        if let Some((d, f, c)) = near
+            && d < r * 2.0
+        {
+            round = Some((f, c));
+            break;
+        }
+    }
+    let (g, on_g) = round.ok_or_else(|| unsupported("the faces at the edge ends must be planar"))?;
+    let cyl = crate::topo::cylinder_face_at(cur, on_g).ok_or_else(|| unsupported("only rounds (cylinders) at the edge ends"))?;
+    if (cyl.radius - r).abs() > 1e-4 * r.max(1.0) || cyl.internal {
+        return Err(unsupported("an edge running into an earlier round of another radius (round both with one radius, or pick them together)"));
+    }
+    let faces = crate::offset::with_same_surface(cur, &[g]);
+    let sharp = crate::delete_face::delete_faces(cur, &faces)?;
+    let mid = (ends[0] + ends[1]) * 0.5;
+    // The restored edge: nearest the middle of the round (its centroid), not its ends (where
+    // the new edge is near too).
+    let old = info.get(g).map(|x| x.centroid).unwrap_or(on_g);
+    UNROUNDING.with(|c| c.set(true));
+    let r2 = blend(&sharp, &[old, mid], r, Shape::Round, what);
+    UNROUNDING.with(|c| c.set(false));
+    r2
+}
+
 pub(crate) fn chamfer_tool(cur: &Body, p: Vec3, s: f64, k: usize) -> Result<Body> {
     chamfer_tool_sides(cur, p, s, None, k)
 }