diff --git a/crates/kernel/src/build.rs b/crates/kernel/src/build.rs
index be65121947..7b65f1d863 100644
--- a/crates/kernel/src/build.rs
+++ b/crates/kernel/src/build.rs
@@ -799,24 +799,61 @@ pub fn extrude_tapered_between(
     smlib_tapered(plane, region, from, to, foot, dir_sign.signum(), taper, corner)
 }
 
-/// [`extrude_tapered_between`] through SMLib's draft extrusion: one loop (SMLib's takes no
-/// holes), its section at `from` the profile offset by the taper, after any straight foot.
+/// [`extrude_tapered_between`] through SMLib's draft extrusion, its section at `from` the
+/// profile offset by the taper, after any straight foot. SMLib's draft extrusion takes one loop:
+/// a region with holes is its outer loop drafted, less each hole drafted the other way (every
+/// wall leaning by the taper on the material's side), refused only where the taper would make a
+/// hole meet the outer wall or another hole within the extrusion.
 #[allow(clippy::too_many_arguments)]
 fn smlib_tapered(plane: &Plane, region: &Region2, from: f64, to: f64, foot: f64, sign: f64, taper: f64, corner: DraftCorner) -> Result<Body> {
-    if !region.holes.is_empty() {
-        return Err(crate::smlib_sweeps::refuse("draft extrusion of a profile with holes (SMLib's takes one loop)"));
-    }
-    let outer = oriented(region)?.map_loops(|l| l.merged_lines(continues_straight)).outer;
-    let bottom = if from == 0.0 || taper == 0.0 {
-        outer
-    } else {
-        let moved = offset_loop(&outer.lp, from * taper.tan())?;
-        let segs: Option<Vec<Seg2>> = moved.into_iter().collect();
+    let joined = oriented(region)?.map_loops(|l| l.merged_lines(continues_straight));
+    // A loop's section `at` along the extrusion: counter-clockwise, grown by `taper` (a hole's
+    // the other way, as the wall of the material round it leans).
+    let section = |l: &NumberedLoop, at: f64, taper: f64| -> Result<NumberedLoop> {
+        let ccw = l.oriented(false);
+        if at == 0.0 || taper == 0.0 {
+            return Ok(ccw);
+        }
+        let segs: Option<Vec<Seg2>> = offset_loop(&ccw.lp, at * taper.tan())?.into_iter().collect();
         let segs = segs.ok_or_else(|| crate::smlib_sweeps::refuse("draft extrusion that starts before its profile where the taper closes a side"))?;
-        NumberedLoop { lp: Loop2 { segs }, from: outer.from }
+        Ok(NumberedLoop { lp: Loop2 { segs }, from: ccw.from })
     };
+    let outer = section(&joined.outer, from, taper)?;
     let draft = (taper != 0.0).then_some(crate::smlib_sweeps::Draft { taper, foot, corner });
-    crate::smlib_sweeps::extrude(plane, &crate::smlib_sweeps::pieces([&bottom]), Some(region), from * sign, to - from, sign, draft)
+    if joined.holes.is_empty() {
+        return crate::smlib_sweeps::extrude(plane, &crate::smlib_sweeps::pieces([&outer]), Some(region), from * sign, to - from, sign, draft);
+    }
+    let Some(draft) = draft else {
+        return Err(KernelError::Invalid("a tapered extrusion needs a taper".into()));
+    };
+    let holes: Vec<NumberedLoop> = joined.holes.iter().map(|h| section(h, from, -taper)).collect::<Result<_>>()?;
+    // The sections where the walls are farthest moved, the two ends: each hole stays inside the
+    // outer loop and clear of the other holes there (the walls are planes, cones and their like,
+    // which move monotonically in between).
+    for at in [from, to] {
+        let o = section(&joined.outer, at, taper)?;
+        let hs: Vec<NumberedLoop> = joined.holes.iter().map(|h| section(h, at, -taper)).collect::<Result<_>>()?;
+        let pts = |l: &NumberedLoop| l.lp.segs.iter().flat_map(|s| s.polyline(1e-3)).collect::<Vec<Vec2>>();
+        // Apart: no point of either inside the other.
+        let apart = |a: &NumberedLoop, b: &NumberedLoop| !pts(a).iter().any(|p| b.lp.contains(*p)) && !pts(b).iter().any(|p| a.lp.contains(*p));
+        for (i, h) in hs.iter().enumerate() {
+            let inside = pts(h).iter().all(|p| o.lp.contains(*p)) && !pts(&o).iter().any(|p| h.lp.contains(*p));
+            if !inside || hs.iter().skip(i + 1).any(|k| !apart(h, k)) {
+                return Err(KernelError::Invalid("the draft makes a hole meet the outer wall or another hole".into()));
+            }
+        }
+    }
+    let all: Vec<NumberedLoop> = std::iter::once(outer.clone()).chain(holes.iter().map(|h| h.oriented(true))).collect();
+    crate::smlib_sweeps::extrude_drafted_with_holes(
+        plane,
+        &crate::smlib_sweeps::pieces([&outer]),
+        &holes.iter().map(|h| crate::smlib_sweeps::pieces([h])).collect::<Vec<_>>(),
+        &crate::smlib_sweeps::pieces(all.iter()),
+        from * sign,
+        to - from,
+        sign,
+        draft,
+    )
 }
 
 /// A planar region on `plane` as the schema 4 record of one face (an open sheet): the plane's
diff --git a/crates/kernel/src/smlib_sweeps.rs b/crates/kernel/src/smlib_sweeps.rs
index 62386961f3..008b981ac3 100644
--- a/crates/kernel/src/smlib_sweeps.rs
+++ b/crates/kernel/src/smlib_sweeps.rs
@@ -71,8 +71,8 @@ pub(crate) struct Draft {
 }
 
 pub(crate) use imp::{
-    body_from_record, curve, extrude, face_section, loft, loft_rails, loft_to_point, path_curve, project_onto_face, revolve, screw, screw_radial,
-    sphere, sweep, sweep_controlled,
+    body_from_record, curve, extrude, extrude_drafted_with_holes, face_section, loft, loft_rails, loft_to_point, path_curve, project_onto_face,
+    revolve, screw, screw_radial, sphere, sweep, sweep_controlled,
 };
 
 /// Refuses what no SMLib sweep does, before any work.
@@ -447,6 +447,79 @@ mod imp {
         with_history(body, &roles, pieces)
     }
 
+    /// The solid `pieces` (one closed loop) on `plane` sweep, moved `from` along its normal and
+    /// drafted `d` over `distance` along `sign` × the normal, as [`extrude`] builds it, without
+    /// its roles.
+    fn drafted_loop(plane: &Plane, pieces: &[Piece], from: f64, distance: f64, sign: f64, d: Draft) -> Result<Brep> {
+        let base = plane.offset(from);
+        let n = plane.x.cross(plane.y).normalized().ok_or_else(|| KernelError::Invalid("profile plane".into()))?;
+        let dir = n * sign.signum();
+        if d.foot > 0.0 {
+            if !(d.foot < distance) {
+                return Err(KernelError::Invalid(format!("taper foot = {}", d.foot)));
+            }
+            let knee = plane.offset(from + sign.signum() * d.foot);
+            let lean = -(distance * d.taper.tan() / (distance - d.foot)).atan();
+            let prism =
+                Brep::extrude(&curves(&base, pieces)?, p(dir), d.foot, 0.0, DraftCorner::default(), true).map_err(|e| failed("extrude", e))?;
+            let slope =
+                Brep::extrude(&curves(&knee, pieces)?, p(dir), distance - d.foot, lean, corner(d.corner), true).map_err(|e| failed("extrude", e))?;
+            let brep = prism.boolean(&slope, solidcraft_smlib::BooleanOp::Union).map_err(|e| failed("extrude", e))?;
+            return brep.ok_or_else(|| failed("extrude", "nothing is left"));
+        }
+        Brep::extrude(&curves(&base, pieces)?, p(dir), distance, -d.taper, corner(d.corner), true).map_err(|e| failed("extrude", e))
+    }
+
+    /// A drafted extrusion of a region with holes: SMLib's draft extrusion takes one loop, so the
+    /// outer loop is drafted and each hole, turned counter-clockwise, is drafted the other way
+    /// and cut from it. Every wall leans by the taper on the material's side, as a single
+    /// drafted sweep would: a taper that narrows the outer boundary widens the holes. `outer` and
+    /// `holes` are the loops' pieces at `from` as [`extrude`] takes them, `all` the region's
+    /// pieces in their numbering (outer, then the holes as they bound the material), which the
+    /// walls' roles name.
+    pub(crate) fn extrude_drafted_with_holes(
+        plane: &Plane,
+        outer: &[Piece],
+        holes: &[Vec<Piece>],
+        all: &[Piece],
+        from: f64,
+        distance: f64,
+        sign: f64,
+        draft: Draft,
+    ) -> Result<Body> {
+        let mut brep = drafted_loop(plane, outer, from, distance, sign, draft)?;
+        for h in holes {
+            let cutter = drafted_loop(plane, h, from, distance, sign, Draft { taper: -draft.taper, ..draft })?;
+            brep = brep
+                .boolean(&cutter, solidcraft_smlib::BooleanOp::Subtract)
+                .map_err(|e| failed("extrude", e))?
+                .ok_or_else(|| KernelError::Invalid("the draft leaves nothing of the profile".into()))?;
+        }
+        let body = body_of(&brep, "extrude")?;
+        let base = plane.offset(from);
+        let top = plane.offset(from + sign.signum() * distance);
+        let low = roles(&body, &base, Some(&top), &seeds(&base, all, |q| q), &[], false)?;
+        let roles: Vec<Role> = if draft.foot > 0.0 {
+            // The sloping walls stand on their edges at the knee, as in [`extrude`].
+            let knee = plane.offset(from + sign.signum() * draft.foot);
+            let high = roles(&body, &knee, Some(&top), &seeds(&knee, all, |q| q), &[], false)?;
+            low.into_iter()
+                .zip(high)
+                .map(|(a, b)| match (a, b) {
+                    (Role::Wall(mut x), Role::Wall(y)) => {
+                        x.extend(y);
+                        Role::Wall(x)
+                    }
+                    (Role::Unknown, w @ Role::Wall(_)) => w,
+                    (a, _) => a,
+                })
+                .collect()
+        } else {
+            low
+        };
+        with_history(body, &roles, all)
+    }
+
     /// The construction sources of a straight extrusion's faces along the normal of `sketch`, as
     /// [`crate::extrude`] gives them: each cap the region at its end (both caps found once
     /// each), each wall swept from one piece that piece as drawn, a line's with the wall's plane.
diff --git a/crates/kernel/src/tests.rs b/crates/kernel/src/tests.rs
index a632470d1f..21abd4d90b 100644
--- a/crates/kernel/src/tests.rs
+++ b/crates/kernel/src/tests.rs
@@ -463,6 +463,21 @@ fn tapered_extrudes() {
     assert!(rel(m.volume, v) < 5e-4, "{} vs {v}", m.volume);
     assert!(m.bbox.max.z < 1e-6 && m.bbox.min.z > -10.0 - 1e-6, "{:?}", m.bbox);
     assert!(extrude_tapered(&Plane::XY, &c, 10.0, 1.0, -60f64.to_radians(), crate::DraftCorner::default()).is_err(), "closes the profile");
+    // The square with a 10 × 10 square hole, 30 up, 5° inward: every wall leans in toward the
+    // material's outside, so the outer frustum narrows and the hole's widens; the solid is the
+    // one frustum less the other, with each wall a face of its own (four out, four in, two caps).
+    let t = 5f64.to_radians().tan();
+    let hole = Loop2::polygon(&[Vec2::new(-5.0, -5.0), Vec2::new(-5.0, 5.0), Vec2::new(5.0, 5.0), Vec2::new(5.0, -5.0)]);
+    let ring = Region2 { outer: sq.outer.clone(), holes: vec![hole] };
+    let b = extrude_tapered(&Plane::XY, &ring, 30.0, 1.0, -5f64.to_radians(), crate::DraftCorner::default()).unwrap();
+    let frustum = |a0: f64, a1: f64| 30.0 / 3.0 * (a0 * a0 + a1 * a1 + a0 * a1);
+    let v = frustum(40.0, 40.0 - 60.0 * t) - frustum(10.0, 10.0 + 60.0 * t);
+    let m = measure(&b).unwrap();
+    assert!(rel(m.volume, v) < 1e-6, "{} vs {v}", m.volume);
+    assert_eq!(m.merged.faces, 10);
+    // At 30° the hole would grow past the outer wall: refused, saying why.
+    let e = extrude_tapered(&Plane::XY, &ring, 30.0, 1.0, -30f64.to_radians(), crate::DraftCorner::default()).unwrap_err();
+    assert!(e.to_string().contains("hole"), "{e}");
 }
 
 /// A slot (two lines and two half-circles, tangent) tapered inward: every edge moves in by