diff --git a/crates/engine/src/boolean_regression_tests.rs b/crates/engine/src/boolean_regression_tests.rs
index 4db35a63..54f0ee80 100644
--- a/crates/engine/src/boolean_regression_tests.rs
+++ b/crates/engine/src/boolean_regression_tests.rs
@@ -1,7 +1,7 @@
 //! Booleans that failed, panicked or hung, replayed from the scripts in
 //! `examples/regressions/` (each script's description says what went wrong).
 
-use serde_json::Value;
+use serde_json::{Value, json};
 
 use crate::Session;
 
@@ -32,3 +32,22 @@ fn shallow_loft_cut_from_the_top_face() {
     let got = volume(&s, "Body1");
     assert!((got - want).abs() < 1e-9 * want, "{got} vs {want}");
 }
+
+#[test]
+fn oblique_cut_through_a_small_arc_matches_a_split() {
+    let scripts = [include_str!("../../../examples/regressions/oblique_cut_of_cylinder.json")];
+    // The same bar split by the prism's tilted top: the piece above it is the cut's result.
+    let mut split = Session::default();
+    let script: Value = serde_json::from_str(scripts[0]).unwrap();
+    let steps = script.get("commands").and_then(Value::as_array).unwrap();
+    split.run_script(&Value::Array(steps[..5].to_vec())).unwrap();
+    let whole = volume(&split, "Tool");
+    split.execute("solid.split_body", &json!({"body": "Tool", "plane": {"origin": [0, -472, 853.91], "normal": [0, 15.44, 40]}})).unwrap();
+    let above = volume(&split, "Tool");
+    assert!(above < whole - 10.0, "{above} of {whole}");
+    for script in scripts {
+        let s = replay(script);
+        let got = volume(&s, "Tool");
+        assert!((got - above).abs() < 1e-6 * above, "{got} vs {above}");
+    }
+}
diff --git a/crates/kernel/src/ops.rs b/crates/kernel/src/ops.rs
index 1b9f9afd..14de038f 100644
--- a/crates/kernel/src/ops.rs
+++ b/crates/kernel/src/ops.rs
@@ -189,11 +189,28 @@ pub fn boolean(a: &Body, b: &Body, op: BoolOp) -> Result<Option<Body>> {
     r
 }
 
+/// Smallest side of the box where the bodies' vertex boxes overlap (infinite when they don't).
+fn meeting_size(a: &Body, b: &Body) -> f64 {
+    let bbox = |x: &Body| {
+        let mut bb = solvecraft_geom::Aabb3::EMPTY;
+        for v in x.solid.vertex_iter() {
+            bb.add(from_p3(v.point()));
+        }
+        bb
+    };
+    let (ba, bb) = (bbox(a), bbox(b));
+    let s = solvecraft_geom::Aabb3 { min: ba.min.max(bb.min), max: ba.max.min(bb.max) }.size();
+    if s.x > 0.0 && s.y > 0.0 && s.z > 0.0 { s.x.min(s.y).min(s.z) } else { f64::INFINITY }
+}
+
 fn boolean_whole(a: &Body, b: &Body, op: BoolOp) -> Result<Option<Body>> {
     a.require_brep("a boolean")?;
     b.require_brep("a boolean")?;
     let size = a.size().max(b.size());
-    let tol_m = size * 5e-4;
+    // The checks mesh both bodies; where they meet in a region much thinner than they are (a
+    // thin part trimmed by a long one), a step from their size would facet the small faces
+    // there coarsely enough to fail the membership test on a correct result.
+    let tol_m = (size * 5e-4).min(meeting_size(a, b) * 2e-3).max(size * 1e-5);
     let meshes = (a.tessellate(tol_m).ok(), b.tessellate(tol_m).ok());
     let (va, vb) = match &meshes {
         (Some(ma), Some(mb)) => (ma.measure().volume, mb.measure().volume),
diff --git a/examples/regressions/oblique_cut_of_cylinder.json b/examples/regressions/oblique_cut_of_cylinder.json
new file mode 100644
index 00000000..3fd277ef
--- /dev/null
+++ b/examples/regressions/oblique_cut_of_cylinder.json
@@ -0,0 +1,15 @@
+{
+ "description": "A thin 437 mm bar whose profile has a 3 mm concave arc, cut by a long prism whose top is tilted 21 degrees to the bar (an elliptical cut through the arc's cylinder). The check on the result meshed both bodies at a step from the 920 mm prism, which faceted the arc so coarsely that a correct cut failed the membership test. Result: the bar with its end trimmed by the tilted plane, as a split by that plane gives.",
+ "commands": [
+  {"command": "sketch.create", "params": {"plane": "XZ", "offset": -462, "name": "Profile"}},
+  {"command": "sketch.line", "params": {"points": [[147.4407, -849.95], [147.4407, -851.0], [151.3952, -851.0], [151.3952, -847.4709], [150.3952, -847.4709]]}},
+  {"command": "sketch.arc.center_point", "params": {"center": [147.4407, -846.95], "start": "l1.start", "end": "l4.end"}},
+  {"command": "sketch.finish", "params": {}},
+  {"command": "solid.extrude", "params": {"sketch": "Profile", "profiles": "all", "direction": "positive", "start_offset": -1, "distance": 437.52, "operation": "new", "body_name": "Tool"}},
+  {"command": "sketch.create", "params": {"plane": "YZ", "name": "Clip"}},
+  {"command": "sketch.line", "params": {"points": [[-472, 853.91], [-432, 838.47], [-432, 820], [-472, 820]], "closed": true}},
+  {"command": "sketch.finish", "params": {}},
+  {"command": "solid.extrude", "params": {"sketch": "Clip", "profiles": "all", "start_offset": -10, "distance": 920, "operation": "new", "body_name": "ClipBody"}},
+  {"command": "solid.combine", "params": {"target": "Tool", "tools": ["ClipBody"], "operation": "cut", "keep_tools": true}}
+ ]
+}