diff --git a/crates/engine/src/naming_history_tests.rs b/crates/engine/src/naming_history_tests.rs
index 97560d42f7..e786049147 100644
--- a/crates/engine/src/naming_history_tests.rs
+++ b/crates/engine/src/naming_history_tests.rs
@@ -691,3 +691,25 @@ fn a_shell_point_pick_moved_off_its_face_reopens_only_that_face() {
     assert!(solid_at(&s, [100.0, 16.0, 10.0]), "the bottom face stays closed");
     assert!(!solid_at(&s, [149.0, 25.0, 10.0]), "the end at x = 150 is open");
 }
+
+/// A two-distance chamfer of a plate's bottom front edge running 220 up the front face, past the
+/// 85 mm where the plate's sides start to taper (rig fillets/5181): the chamfer takes up the front
+/// face's straight side edges too, and lies between their faces, but it is made from the picked
+/// edge alone. Its one face has the picked edge's name everywhere on it (it was named after the
+/// left side's edge, l6, the first edge it took up).
+#[test]
+fn a_chamfer_running_past_the_side_edges_it_takes_up_is_named_by_its_edge() {
+    let mut s = Session::default();
+    run(&mut s, "sketch.create", json!({"plane": {"origin": [0, 0, 0], "x_dir": [1, 0, 0], "y_dir": [0, 0, 1]}, "name": "Bracket"}));
+    let taper = 30.675635228421154;
+    run(&mut s, "sketch.line", json!({"points": [[-50, 0], [50, 0], [50, 85], [taper, 222.5], [-taper, 222.5], [-50, 85]], "closed": true}));
+    run(&mut s, "sketch.finish", json!({}));
+    run(&mut s, "solid.extrude", json!({"sketch": "Bracket", "distance": 23, "body_name": "Bracket"}));
+    run(&mut s, "solid.chamfer", json!({"edges": [[0, 0, 0]], "distance": 220, "distance2": 11}));
+    let blends: Vec<String> = names(&s, "Bracket").into_iter().map(|(n, _)| n).filter(|n| n.starts_with("F3:blend:")).collect();
+    assert_eq!(blends, vec!["F3:blend:F2:side:l1|F2:start".to_string()]);
+    // On the chamfer's plane, through (x, -11, 0) and (x, 0, 220): below and above z = 85.
+    let on = |z: f64| Vec3::new(0.0, -11.0 * (1.0 - z / 220.0), z);
+    let at = solidcraft_doc::naming::face_names_at(&s.model.state(), &[on(40.0), on(150.0)]);
+    assert_eq!(at, vec![blends[0].clone(), blends[0].clone()]);
+}
diff --git a/crates/kernel/src/blend_smlib.rs b/crates/kernel/src/blend_smlib.rs
index 1e6e7e10f7..0f197e43ca 100644
--- a/crates/kernel/src/blend_smlib.rs
+++ b/crates/kernel/src/blend_smlib.rs
@@ -362,8 +362,8 @@ mod imp {
                 (Some(o), Some(ro)) => match r.history().map_err(|e| failed(what, "history", e))?.history(&[o], ro) {
                     Ok(mut h) => {
                         let operand = History::identity(body).edges;
-                        let replaced = blended(body, edges, &h);
-                        solidcraft_smlib::history::blends(&mut h, &operand, &replaced);
+                        let taken_up = taken_up(body, edges, &h);
+                        solidcraft_smlib::history::blends(&mut h, &operand, edges, &taken_up);
                         Some(with_corners(h))
                     }
                     Err(e) => {
@@ -414,10 +414,10 @@ mod imp {
         h
     }
 
-    /// The operand's edges the blend replaced: each picked edge, and every edge no result edge
-    /// comes from (one the blend's corners took up), in the operand's edge order.
-    fn blended(body: &Body, picked: &[usize], h: &History) -> Vec<usize> {
-        let mut out: BTreeSet<usize> = picked.iter().copied().collect();
+    /// The operand's edges the blend took up besides the picked ones: every edge no result edge
+    /// comes from (one the blend's corners took up, or one it ran over), in the operand's edge
+    /// order.
+    fn taken_up(body: &Body, picked: &[usize], h: &History) -> Vec<usize> {
         let kept: BTreeSet<usize> = h
             .edges
             .iter()
@@ -427,8 +427,7 @@ mod imp {
                 _ => None,
             })
             .collect();
-        out.extend((0..body.edge_count()).filter(|e| !kept.contains(e)));
-        out.into_iter().collect()
+        (0..body.edge_count()).filter(|e| !kept.contains(e) && !picked.contains(e)).collect()
     }
 }
 
diff --git a/crates/smlib/src/history.rs b/crates/smlib/src/history.rs
index 5ad04c3a9b..b88b54d128 100644
--- a/crates/smlib/src/history.rs
+++ b/crates/smlib/src/history.rs
@@ -202,13 +202,17 @@ impl Raw {
     }
 }
 
-/// A blend's faces (fillet, chamfer) in `h`, the history of a blend of edges `blended` of its
+/// A blend's faces (fillet, chamfer) in `h`, the history of a blend of edges `picked` of its
 /// one operand (operand 0), whose own edges `operand` lists (the faces each bounds, as in the
-/// operand's identity history): SMLib makes a blend face with no tag, so each Generated face is
-/// given [`FaceOrigin::Edge`] for every blended edge whose two faces both lie under faces next
-/// to it and no longer meet each other directly. A corner patch between several blends matches
-/// none of them and stays without origin.
-pub fn blends(h: &mut History, operand: &[EdgeProv], blended: &[usize]) {
+/// operand's identity history), which also took up edges `taken_up` (no result edge comes from
+/// them: a corner's short edge, or an edge the blend ran over): SMLib makes a blend face with no
+/// tag, so each Generated face is given [`FaceOrigin::Edge`] for every picked edge whose two
+/// faces both lie under faces next to it and no longer meet each other directly, and only where
+/// no picked edge is such, every taken-up edge that is. A chamfer running up past the end of the
+/// face beside it takes up that face's side edge and lies between its faces too: it is made from
+/// the picked edge alone. A corner patch between several blends matches none of them and stays
+/// without origin.
+pub fn blends(h: &mut History, operand: &[EdgeProv], picked: &[usize], taken_up: &[usize]) {
     let mut next_to: Vec<BTreeSet<FaceOrigin>> = vec![BTreeSet::new(); h.faces.len()];
     for e in &h.edges {
         for f in &e.faces {
@@ -238,14 +242,18 @@ pub fn blends(h: &mut History, operand: &[EdgeProv], blended: &[usize]) {
         if f.change != Change::Generated || !f.origins.is_empty() {
             continue;
         }
-        let edges = blended.iter().filter(|e| {
+        let under = |e: &&usize| {
             operand.get(**e).is_some_and(|p| {
                 let [a, b] = p.faces.as_slice() else { return false };
                 let (a, b) = (FaceOrigin::Face { operand: 0, face: *a }, FaceOrigin::Face { operand: 0, face: *b });
                 around.contains(&a) && around.contains(&b) && !meeting.contains(&(a.min(b), a.max(b)))
             })
-        });
-        f.origins = edges.map(|e| FaceOrigin::Edge { operand: 0, edge: *e }).collect();
+        };
+        let mut edges: Vec<usize> = picked.iter().filter(under).copied().collect();
+        if edges.is_empty() {
+            edges = taken_up.iter().filter(under).copied().collect();
+        }
+        f.origins = edges.into_iter().map(|e| FaceOrigin::Edge { operand: 0, edge: e }).collect();
     }
 }
 
diff --git a/crates/smlib/src/history/tests.rs b/crates/smlib/src/history/tests.rs
index 06ecf734bf..6fdc4b9944 100644
--- a/crates/smlib/src/history/tests.rs
+++ b/crates/smlib/src/history/tests.rs
@@ -96,7 +96,7 @@ fn a_fillet_face_comes_from_its_edge() {
     let mut h = History { operands: 1, faces, edges: vec![edge(4, 6), edge(5, 6), edge(0, 6), edge(2, 6), edge(0, 4)] };
     // The operand's own edges: edge 0 between faces 4 and 5, edge 1 between 0 and 4.
     let operand = vec![edge(4, 5), edge(0, 4)];
-    blends(&mut h, &operand, &[0, 1]);
+    blends(&mut h, &operand, &[0], &[1]);
     assert_eq!(h.faces[6].origins, vec![FaceOrigin::Edge { operand: 0, edge: 0 }]);
     assert!(h.faces[..6].iter().all(|f| f.origins.len() == 1));
 }
diff --git a/tests/kernel-cases/fillets/5181-two-distance-chamfer-runs-past-tapered-sides/expected.json b/tests/kernel-cases/fillets/5181-two-distance-chamfer-runs-past-tapered-sides/expected.json
index dde396198d..0550322981 100644
--- a/tests/kernel-cases/fillets/5181-two-distance-chamfer-runs-past-tapered-sides/expected.json
+++ b/tests/kernel-cases/fillets/5181-two-distance-chamfer-runs-past-tapered-sides/expected.json
@@ -2,7 +2,7 @@
  "sources": [
   "tangency-labs/solidcraft#5181"
  ],
- "what": "a 220 x 11 two-distance chamfer along the bottom edge of a 23 mm plate 100 wide whose sides run straight for 85 mm and then taper to 61.4 at 222.5: refused ('runs past the faces beside the edge into other geometry; the largest size that fits is 85 mm')",
+ "what": "a 220 x 11 two-distance chamfer along the bottom edge of a 23 mm plate 100 wide whose sides run straight for 85 mm and then taper to 61.4 at 222.5: it builds, the chamfer plane running on past the straight sides into the tapered ones, which it trims",
  "source": "analytic",
  "method": "the plate (profile 100x85 + the trapezoid to 61.351 at 222.5) x 23. The first face is the big face (it faces up most: horizontal, the bottom faces down): 220 up it, 11 into the bottom face. The chamfer plane cuts the wedge 11 (1 - z/220) deep across the full width w(z) (100, then tapering past z = 85): Int_0^220 w(z) 11 (1 - z/220) dz, the tapered sides simply trimmed",
  "body_count": 1,