diff --git a/crates/engine/src/sample.rs b/crates/engine/src/sample.rs
index 8353a58..7ef03ca 100644
--- a/crates/engine/src/sample.rs
+++ b/crates/engine/src/sample.rs
@@ -821,6 +821,38 @@ mod tests {
         }
     }
 
+    /// The one-to-one sweep and the crank (#444). The arm's profile extruded alone is a
+    /// one-to-one sweep (one source, one target) and sweeps all-hex as well as extrude does. The
+    /// crank itself ends at several levels (pocket floor at 8 mm, arm 16, pedal boss 20, spindle
+    /// boss 22), so no one-to-one sweep takes it: the sweep says so, naming a cap only part of a
+    /// ring reaches, where it reported a "linking face with no top side"; extrude meshes it.
+    #[test]
+    fn the_sweep_takes_the_arm_profile_and_names_the_crank_levels() {
+        let session = |script: &str| {
+            let bytes = fieldcraft_geometry::script_design(script).unwrap();
+            let (dir, path) = crate::tests::design_file(&bytes);
+            let mut s = Session::default();
+            s.execute("geometry.open", &json!({"path": path})).unwrap();
+            (dir, s)
+        };
+        let quality = |s: &mut Session, method: &str| -> crate::Result<f64> {
+            let r = s.execute("mesh.hex.generate", &json!({"body": "CrankArm", "size": 3, "method": method}))?;
+            assert_eq!(r["bodies"][0]["method"], method, "{r}");
+            Ok(r["bodies"][0]["quality"]["min_scaled_jacobian"].as_f64().unwrap())
+        };
+        // The script up to the arm's extrusion: the profile alone.
+        let end = CRANK_ARM.find("{\"command\": \"solid.cylinder\"").unwrap();
+        let profile = format!("{}]}}", CRANK_ARM[..end].trim_end().trim_end_matches(','));
+        let (_dir, mut s) = session(&profile);
+        let (sweep, extrude) = (quality(&mut s, "sweep").unwrap(), quality(&mut s, "extrude").unwrap());
+        assert!(sweep > 0.3 && sweep > 0.95 * extrude, "sweep {sweep}, extrude {extrude}");
+
+        let (_dir, mut s) = session(CRANK_ARM);
+        let e = quality(&mut s, "sweep").unwrap_err().to_string();
+        assert!(e.contains("is parallel to the source and only part of the ring reaches it") && e.contains("method `extrude`"), "{e}");
+        assert!(quality(&mut s, "extrude").unwrap() > 0.35);
+    }
+
     /// `file.sample NAME`, checked clean: ready, no errors or warnings.
     fn open(name: &str) -> Session {
         let mut s = Session::default();
diff --git a/crates/mesh/src/hex/sweep.rs b/crates/mesh/src/hex/sweep.rs
index 0800c76..ba40e05 100644
--- a/crates/mesh/src/hex/sweep.rs
+++ b/crates/mesh/src/hex/sweep.rs
@@ -33,7 +33,7 @@ use super::region;
 use super::{Ctx, Raw, project_to_face, project_to_faces};
 use crate::quad::transfinite_grid;
 use crate::size::ideal_divisions;
-use crate::vec3::{P, sub};
+use crate::vec3::{P, dot, sub};
 use crate::{Error, Result};
 
 /// The most source faces tried.
@@ -118,7 +118,10 @@ fn topology(brep: &Brep, s: usize) -> std::result::Result<Topology, String> {
                     run.push((e, fwd));
                     k += 1;
                 }
-                ring.push(link(brep, f, &run)?);
+                ring.push(link(brep, f, &run).map_err(|e| match cap(brep, s, f) {
+                    Some(why) => why,
+                    None => e,
+                })?);
             }
             used.extend(ring.iter().map(|l| l.face));
             front = ring.iter().flat_map(|l| l.top.iter().map(move |&(e, fwd)| (e, fwd, l.face))).collect();
@@ -140,6 +143,21 @@ fn topology(brep: &Brep, s: usize) -> std::result::Result<Topology, String> {
     Ok(Topology { source: s, target, rings })
 }
 
+/// Why face `f`, reached from a front swept from source `s`, cannot be a linking face when it is
+/// a plane parallel to the source: a cap that only part of the ring reaches. The body then ends
+/// at several levels (a step, a boss, a pocket floor), which no one-to-one sweep takes; saying so
+/// names the reason where the linking-face split would only report the symptom (#444).
+fn cap(brep: &Brep, s: usize, f: usize) -> Option<String> {
+    let (_, ns) = brep.faces.get(s)?.plane?;
+    let (_, nf) = brep.faces.get(f)?.plane?;
+    (dot(ns, nf).abs() > 1.0 - 1e-9).then(|| {
+        format!(
+            "face {} is parallel to the source and only part of the ring reaches it: the body ends at more than one level (a step, a boss or a pocket), and a one-to-one sweep has one target face; method `extrude` meshes such bodies level by level",
+            brep.face_tag(f)
+        )
+    })
+}
+
 /// Whether the front's edges are exactly one loop of face `t`.
 fn is_loop_of(brep: &Brep, t: usize, front: &[(usize, bool, usize)]) -> bool {
     let edges: BTreeSet<usize> = front.iter().map(|x| x.0).collect();