diff --git a/crates/engine/src/boolean_regression_tests.rs b/crates/engine/src/boolean_regression_tests.rs
index 6efbc8f5f7..76910333cc 100644
--- a/crates/engine/src/boolean_regression_tests.rs
+++ b/crates/engine/src/boolean_regression_tests.rs
@@ -582,16 +582,24 @@ fn oblique_cuts_through_a_chamfered_ring_are_exact() {
     let script: Value = serde_json::from_str(include_str!("../../../examples/regressions/oblique_cuts_through_chamfered_ring.json")).unwrap();
     let steps = script.get("commands").and_then(Value::as_array).unwrap();
     let mut s = Session::default();
-    let mut volumes = Vec::new();
+    // The ring after the move and after each cut, and what each cut took away (the ring before it
+    // less the ring after it: a small body that measures to its own accuracy, where the difference
+    // of the whole ring's volumes is lost in the integration's 1e-6 of 1149 mm³).
+    let mut rings: Vec<solidcraft_kernel::Body> = Vec::new();
     for step in steps {
         let reply = s.execute(step["command"].as_str().unwrap(), &step["params"]).unwrap();
         if step["command"] == "solid.extrude" {
             assert!(reply["warning"].is_null(), "{reply}");
         }
         if matches!(step["command"].as_str(), Some("solid.move" | "solid.extrude")) {
-            volumes.push(s.model.state().body("R").unwrap().body.mesh(&solidcraft_kernel::MeshTolerance::chord(1e-5)).unwrap().measure().volume);
+            rings.push(s.model.state().body("R").unwrap().body.clone());
         }
     }
+    let taken = |k: usize| -> f64 {
+        let piece = solidcraft_kernel::boolean(&rings[k], &rings[k + 1], solidcraft_kernel::BoolOp::Cut).unwrap().unwrap();
+        solidcraft_kernel::measure(&piece).unwrap().volume
+    };
+    let volumes: Vec<f64> = rings.iter().map(|b| b.mesh(&solidcraft_kernel::MeshTolerance::chord(1e-5)).unwrap().measure().volume).collect();
     // Pappus: the profile's moment about the axis turned through 240°.
     let profile = [(16.6, 0.0), (17.5, 0.0), (18.5, 1.0), (18.5, 7.0), (17.5, 8.0), (16.6, 8.0), (16.4, 7.8), (16.4, 0.2)];
     let moment: f64 = (0..profile.len())
@@ -601,14 +609,14 @@ fn oblique_cuts_through_a_chamfered_ring_are_exact() {
         })
         .sum();
     let ring = moment.abs() * 4.0 * std::f64::consts::PI / 3.0;
-    let [whole, first, second, notched] = volumes[..] else { panic!("{volumes:?}") };
+    let [whole, _, _, _] = volumes[..] else { panic!("{volumes:?}") };
     // Volumes from meshes at 1e-5 mm: within a few millionths of the ring's.
     assert!((whole - ring).abs() < 1e-5 * ring, "{whole} vs {ring}");
     // The ring and the two prisms are mirror images across XZ.
-    let (cut1, cut2) = (whole - first, first - second);
-    assert!(cut1 > 5.0 && (cut1 - cut2).abs() < 1e-6, "{cut1} vs {cut2}");
-    let notch = ring_notch();
-    assert!(((second - notched) - notch).abs() < 1e-4, "{} vs {notch}", second - notched);
+    let (cut1, cut2) = (taken(0), taken(1));
+    assert!(cut1 > 5.0 && (cut1 - cut2).abs() < 1e-6 * cut1, "{cut1} vs {cut2}");
+    let (notched, notch) = (taken(2), ring_notch());
+    assert!((notched - notch).abs() < 1e-5 * notch, "{notched} vs {notch}");
     let state = s.model.state();
     let body = &state.body("R").unwrap().body;
     assert!(body.validity().is_empty(), "{:?}", body.validity());
@@ -621,8 +629,7 @@ fn oblique_cuts_through_a_chamfered_ring_are_exact() {
     );
     assert!(coarse < fine && coarse > fine - 2.0, "area meshed at 0.05: {coarse} vs {fine}");
     println!(
-        "ring {whole:.6} / {ring:.6} mm³; cuts {cut1:.6}, {cut2:.6}; notch {:.6} / {notch:.6}; area meshed at 0.05 {coarse:.4} / {fine:.4}",
-        second - notched
+        "ring {whole:.6} / {ring:.6} mm³; cuts {cut1:.6}, {cut2:.6}; notch {notched:.6} / {notch:.6}; area meshed at 0.05 {coarse:.4} / {fine:.4}"
     );
 }
 
@@ -634,17 +641,18 @@ fn notch_into_a_ring_chamfer_is_cut_exactly() {
     let script: Value = serde_json::from_str(include_str!("../../../examples/regressions/oblique_cuts_through_chamfered_ring.json")).unwrap();
     let steps = script.get("commands").and_then(Value::as_array).unwrap();
     let mut s = Session::default();
-    let measure =
-        |s: &Session| s.model.state().body("R").unwrap().body.mesh(&solidcraft_kernel::MeshTolerance::chord(1e-5)).unwrap().measure().volume;
     s.run_script(&Value::Array(steps[..5].to_vec())).unwrap();
-    let before = measure(&s);
+    let before = s.model.state().body("R").unwrap().body.clone();
     // The notch's sketch and its cut.
     for step in &steps[steps.len() - 4..] {
         let reply = s.execute(step["command"].as_str().unwrap(), &step["params"]).unwrap();
         assert!(reply["warning"].is_null(), "{reply}");
     }
-    let (got, want) = (before - measure(&s), ring_notch());
-    assert!((got - want).abs() < 1e-4, "{got} vs {want}");
+    // What the cut took: the ring before it less the ring after it, measured as a body of its own
+    // (the difference of the two rings' volumes is lost in the integration's 1e-6 of 1149 mm³).
+    let piece = solidcraft_kernel::boolean(&before, &s.model.state().body("R").unwrap().body, solidcraft_kernel::BoolOp::Cut).unwrap().unwrap();
+    let (got, want) = (solidcraft_kernel::measure(&piece).unwrap().volume, ring_notch());
+    assert!((got - want).abs() < 1e-5 * want, "{got} vs {want}");
 }
 
 /// What the ring's notch takes: a band 0.9 wide about a radius, from 17.6 out along it, and from