diff --git a/crates/engine/src/cmd/draw2.rs b/crates/engine/src/cmd/draw2.rs
index 5d955696..ea4439ce 100644
--- a/crates/engine/src/cmd/draw2.rs
+++ b/crates/engine/src/cmd/draw2.rs
@@ -3,7 +3,7 @@
 
 use std::sync::Arc;
 
-use kurbo::{ParamCurve, ParamCurveNearest};
+use kurbo::{CubicBez, ParamCurve, ParamCurveNearest};
 use serde_json::{Value, json};
 use vectorcraft_color::{Color, Paint};
 use vectorcraft_doc::{Appearance, Document, Node, NodeId, NodeKind, PressureProfile, Selection};
@@ -1048,17 +1048,46 @@ fn smooth_subpath(sp: &SubPath, near: &dyn Fn(Point) -> bool, tol: f64) -> Optio
         open.anchors.push(open.anchors[0]);
         m.push(false);
         open.closed = false;
-        let mut res = smooth_open(&open.anchors, &m, tol);
+        let mut res = smooth_open(&open.anchors, &m, near, tol);
         let l = res.pop()?;
         if let Some(r0) = res.first_mut() {
             r0.h_in = l.h_in;
         }
         return Some(SubPath::new(res, true));
     }
-    Some(SubPath::new(smooth_open(&sp.anchors, &marked, tol), false))
+    Some(SubPath::new(smooth_open(&sp.anchors, &marked, near, tol), false))
 }
 
-fn smooth_open(anchors: &[Anchor], marked: &[bool], tol: f64) -> Vec<Anchor> {
+/// The segment `c`, which ends in the drag's reach (`near`) and starts outside it, split where it
+/// enters the reach: the part outside, then the part in reach. `None` when no more than a sliver
+/// is outside.
+fn split_at_reach(c: CubicBez, near: &dyn Fn(Point) -> bool) -> Option<(CubicBez, CubicBez)> {
+    const STEPS: u32 = 32;
+    let step = 1.0 / f64::from(STEPS);
+    // Back from the end in reach to the first sample outside, then halving to the crossing.
+    let outside = (1..=STEPS).map(|i| 1.0 - f64::from(i) * step).find(|t| !near(c.eval(*t)))?;
+    let (mut lo, mut hi) = (outside, outside + step);
+    for _ in 0..20 {
+        let mid = (lo + hi) / 2.0;
+        if near(c.eval(mid)) {
+            hi = mid;
+        } else {
+            lo = mid;
+        }
+    }
+    // A straight segment's parts stay straight, their handles on their ends.
+    let straight = c.p1 == c.p0 && c.p2 == c.p3;
+    let part = |range| {
+        let s = c.subsegment(range);
+        if straight { CubicBez::new(s.p0, s.p0, s.p3, s.p3) } else { s }
+    };
+    (hi > 0.02).then(|| (part(0.0..hi), part(hi..1.0)))
+}
+
+/// `anchors` with each run of `marked` ones refitted, together with the stretch of the segments
+/// leading into the run that is in the drag's reach (`near`): a short drag smooths what is under
+/// it, and the rest of a long segment next to it stays as it was (#1512).
+fn smooth_open(anchors: &[Anchor], marked: &[bool], near: &dyn Fn(Point) -> bool, tol: f64) -> Vec<Anchor> {
     let n = anchors.len();
     let mut runs = vec![];
     let mut i = 0;
@@ -1079,8 +1108,27 @@ fn smooth_open(anchors: &[Anchor], marked: &[bool], tol: f64) -> Vec<Anchor> {
         if hi - lo < 2 {
             continue;
         }
-        let new = refit_run(&out[lo..=hi], tol);
-        out.splice(lo..=hi, new);
+        let mut piece = out[lo..=hi].to_vec();
+        // The anchors outside the reach, kept with the part of their segment that is outside.
+        let (mut head, mut tail) = (None, None);
+        if hi > b
+            && let [.., inner, outer] = piece.as_mut_slice()
+            && let Some((far, reach)) = split_at_reach(CubicBez::new(outer.p, outer.h_in, inner.h_out, inner.p), near)
+        {
+            inner.h_out = reach.p2;
+            tail = Some(Anchor { h_in: far.p1, ..*outer });
+            *outer = Anchor::with_handles(far.p3, reach.p1, far.p2);
+        }
+        if lo < a
+            && let [outer, inner, ..] = piece.as_mut_slice()
+            && let Some((far, reach)) = split_at_reach(CubicBez::new(outer.p, outer.h_out, inner.h_in, inner.p), near)
+        {
+            inner.h_in = reach.p2;
+            head = Some(Anchor { h_out: far.p1, ..*outer });
+            *outer = Anchor::with_handles(far.p3, far.p2, reach.p1);
+        }
+        let new = refit_run(&piece, tol);
+        out.splice(lo..=hi, head.into_iter().chain(new).chain(tail));
     }
     out
 }
diff --git a/crates/engine/src/tests_draw2.rs b/crates/engine/src/tests_draw2.rs
index f31d422b..d55370b1 100644
--- a/crates/engine/src/tests_draw2.rs
+++ b/crates/engine/src/tests_draw2.rs
@@ -412,6 +412,29 @@ fn smooth_tool_reduces_jagged_path() {
     assert_eq!(p.subpaths[0].anchors[0].p, Point::new(100.0, 200.0));
 }
 
+/// #1512: a short drag over a small bump smooths the stretch of path under it. The long straight
+/// sides next to the bump stay straight lines from their far ends, which keep their place.
+#[test]
+fn a_short_smooth_drag_leaves_the_rest_of_long_segments_alone() {
+    let mut s = session();
+    let anchors: Vec<_> =
+        [(50.0, 200.0), (190.0, 200.0), (200.0, 192.0), (210.0, 200.0), (350.0, 200.0)].map(|(x, y)| json!({"x": x, "y": y})).to_vec();
+    let r = s.execute("path.create", &json!({"anchors": anchors})).unwrap();
+    let id = NodeId(r["id"].as_u64().unwrap());
+    let before = path(&s, id);
+    drag(&mut s, "smooth", &[(195.0, 194.0), (205.0, 194.0)], Mods::default());
+    let p = path(&s, id);
+    assert_ne!(p, before, "the bump is smoothed");
+    let a = &p.subpaths[0].anchors;
+    let (first, second, last) = (a[0], a[1], a[a.len() - 1]);
+    assert!(first.p == Point::new(50.0, 200.0) && !first.has_out() && !second.has_in(), "the left side is a line still: {first:?} {second:?}");
+    assert!(last.p == Point::new(350.0, 200.0) && !last.has_in() && !a[a.len() - 2].has_out(), "and the right one: {last:?}");
+    // Every other anchor is within the tool's reach of the drag (12 px either way).
+    for x in &a[1..a.len() - 1] {
+        assert!((182.0..=218.0).contains(&x.p.x) && (190.0..=201.0).contains(&x.p.y), "{x:?}");
+    }
+}
+
 #[test]
 fn join_tool_joins_two_lines() {
     let mut s = session();
diff --git a/crates/geom/src/corners.rs b/crates/geom/src/corners.rs
index 209010d3..31e03026 100644
--- a/crates/geom/src/corners.rs
+++ b/crates/geom/src/corners.rs
@@ -155,8 +155,8 @@ impl Corner {
         let (h_out, h_in) = match kind {
             // An arc tangent to both sides, turning by 180° less the angle between them there.
             CornerKind::Round => {
-                let h = radius * arc_handle(-cos);
-                (start - du * h, end - dv * h)
+                let (hu, hv) = self.round_handles(radius, (start, du), (end, dv));
+                (start - du * hu, end - dv * hv)
             }
             // An arc centred on the corner through both ends, spanning the angle.
             CornerKind::InvertedRound => {
@@ -169,6 +169,33 @@ impl Corner {
     }
 }
 
+impl Corner {
+    /// The handle lengths of a round cut of `radius` between `start` and `end` (each a point and
+    /// the direction its side runs on in there). Between straight sides they are the arc's. A
+    /// curved side has turned by the time the cut meets it, so the arc's handles would reach past
+    /// where the tangents at the cut's ends cross and the cut would stick out of the corner
+    /// (#1512): there each handle is the share an arc takes of its tangent, up to that crossing
+    /// (a third of the way to the other end where the tangents don't cross between them).
+    fn round_handles(&self, radius: f64, (start, du): (Point, Vec2), (end, dv): (Point, Vec2)) -> (f64, f64) {
+        let cos = du.dot(dv);
+        let arc = arc_handle(-cos);
+        if self.side_u.straight() && self.side_v.straight() {
+            return (radius * arc, radius * arc);
+        }
+        // start − du·a = end − dv·b is where the tangents cross.
+        let (cross, w) = (du.cross(dv), start - end);
+        let (a, b) = (w.cross(dv) / cross, w.cross(du) / cross);
+        if cross.abs() > MIN_SINE && a > EPS && b > EPS && a.is_finite() && b.is_finite() {
+            // An arc's handle over its tangent's length, radius · tan(turn / 2).
+            let share = arc * (1.0 - cos) / cross.abs();
+            (a * share, b * share)
+        } else {
+            let third = start.distance(end) / 3.0;
+            (third, third)
+        }
+    }
+}
+
 /// A corner cut: the parameters where it meets its sides (from the corner), its two new anchors
 /// and the handles between them.
 #[derive(Clone, Copy, Debug)]
@@ -401,6 +428,30 @@ mod tests {
         }
     }
 
+    /// A round cut next to a curve stays inside its corner, however large (#1512): its handles
+    /// stop short of where the tangents at its ends cross, so it doesn't stick out past the sides.
+    #[test]
+    fn a_round_cut_next_to_a_curve_stays_inside_its_corner() {
+        // A square whose top side arches up, meeting the upright sides at an angle.
+        let mut sp =
+            SubPath::polyline(&[Point::new(100.0, 150.0), Point::new(300.0, 150.0), Point::new(300.0, 300.0), Point::new(100.0, 300.0)], true);
+        sp.anchors[0].h_out = Point::new(120.0, 20.0);
+        sp.anchors[1].h_in = Point::new(280.0, 20.0);
+        let path = PathData::single(sp);
+        let bounds = path.bounds().unwrap().inflate(1e-6, 1e-6);
+        for radius in [10.0, 60.0, 200.0, 1e6] {
+            let (cut, _) = cut_corners(&path, &[radius, radius], &[]);
+            let b = cut.bounds().unwrap();
+            assert!(bounds.union(b) == bounds, "radius {radius}: {b:?} is outside {bounds:?}");
+            // Each cut's handles end before its tangents cross: the cut turns one way only.
+            let a = &cut.subpaths[0].anchors;
+            for (from, to) in [(a[a.len() - 1], a[0]), (a[1], a[2])] {
+                let (t0, t1, chord) = (from.h_out - from.p, to.p - to.h_in, to.p - from.p);
+                assert!(t0.cross(chord) * chord.cross(t1) > 0.0 && t0.cross(t1) * t0.cross(chord) > 0.0, "radius {radius}: {from:?} {to:?}");
+            }
+        }
+    }
+
     /// Inverted round and chamfer cuts end where the round one does, at any angle.
     #[test]
     fn kinds_share_their_ends() {