diff --git a/crates/ui-egui/src/icons.rs b/crates/ui-egui/src/icons.rs
index 41368628..976e58ab 100644
--- a/crates/ui-egui/src/icons.rs
+++ b/crates/ui-egui/src/icons.rs
@@ -146,6 +146,8 @@ impl Pen16<'_> {
         let v: Vec<Pos2> = pts.iter().map(|(x, y)| self.p(*x, *y)).collect();
         self.painter.add(PathShape::closed_line(v, PathStroke::new(self.width * self.s(), self.color)));
     }
+    /// Fill a **convex** outline: the tessellator fans a concave one into slivers across its
+    /// notches, so a concave glyph is drawn as overlapping convex pieces (see [`SELECTION_ARROW`]).
     fn fill(&self, pts: &[(f32, f32)]) {
         let v: Vec<Pos2> = pts.iter().map(|(x, y)| self.p(*x, *y)).collect();
         self.painter.add(PathShape::convex_polygon(v, self.color, Stroke::NONE));
@@ -205,6 +207,25 @@ impl Pen16<'_> {
     }
 }
 
+/// The convex pieces of each concave filled glyph. Pieces overlap rather than abut: abutting
+/// antialiased edges would leave a faint seam.
+type Pieces = &'static [&'static [(f32, f32)]];
+
+/// The Selection tool's arrow pointer (tip upper left, a notch each side of the tail): the head
+/// with its left wing, the right wing, and the tail. Only the head reaches the tip: slivers
+/// meeting there would antialias into a spike past it.
+const SELECTION_ARROW: Pieces = &[
+    &[(4.5, 2.0), (4.5, 13.0), (7.2, 10.5), (10.1, 7.39)],
+    &[(7.5, 9.0), (8.9, 9.9), (12.5, 9.7), (10.1, 7.39)],
+    &[(7.8, 8.6), (7.2, 10.5), (9.2, 14.6), (10.8, 13.9), (8.9, 9.9)],
+];
+/// A loudspeaker: the magnet box, running a little into the cone.
+const SPEAKER: Pieces = &[&[(2.0, 6.0), (5.5, 6.0), (5.5, 10.0), (2.0, 10.0)], &[(5.0, 6.0), (9.0, 2.5), (9.0, 13.5), (5.0, 10.0)]];
+/// A four-pointed star: an upright and a level diamond, whose edges cross at the inner corners.
+const SPARKLE: Pieces = &[&[(8.0, 1.5), (9.784, 8.0), (8.0, 14.5), (6.216, 8.0)], &[(1.5, 8.0), (8.0, 6.216), (14.5, 8.0), (8.0, 9.784)]];
+#[cfg(test)]
+const CONCAVE: [Pieces; 3] = [SELECTION_ARROW, SPEAKER, SPARKLE];
+
 /// Paint `icon` centred in `rect`.
 pub fn paint(painter: &Painter, rect: Rect, icon: Icon, color: Color32) {
     let pen = Pen16 { painter, rect, color, width: 1.25 };
@@ -214,7 +235,7 @@ pub fn paint(painter: &Painter, rect: Rect, icon: Icon, color: Color32) {
             pen.closed(&[(2.5, 7.5), (8.0, 2.5), (13.5, 7.5), (13.5, 13.5), (2.5, 13.5)]);
             pen.rect(6.5, 9.5, 9.5, 13.5);
         }
-        Selection => pen.fill(&[(4.5, 2.0), (4.5, 13.0), (7.2, 10.5), (9.2, 14.6), (10.8, 13.9), (8.9, 9.9), (12.5, 9.7)]),
+        Selection => SELECTION_ARROW.iter().for_each(|p| pen.fill(p)),
         Hand => {
             pen.line(&[(5.0, 9.0), (5.0, 4.0)]);
             pen.line(&[(7.3, 8.0), (7.3, 2.6)]);
@@ -358,7 +379,7 @@ pub fn paint(painter: &Painter, rect: Rect, icon: Icon, color: Color32) {
             pen.dot(8.0, 8.0, 2.2);
         }
         Speaker => {
-            pen.fill(&[(2.0, 6.0), (5.0, 6.0), (9.0, 2.5), (9.0, 13.5), (5.0, 10.0), (2.0, 10.0)]);
+            SPEAKER.iter().for_each(|p| pen.fill(p));
             pen.arc(9.0, 8.0, 3.0, -50.0, 50.0);
             pen.arc(9.0, 8.0, 5.5, -50.0, 50.0);
         }
@@ -634,7 +655,7 @@ pub fn paint(painter: &Painter, rect: Rect, icon: Icon, color: Color32) {
             pen.line(&[(9.4, 2.8), (6.6, 13.2)]);
         }
         Sparkle => {
-            pen.fill(&[(8.0, 1.5), (9.4, 6.6), (14.5, 8.0), (9.4, 9.4), (8.0, 14.5), (6.6, 9.4), (1.5, 8.0), (6.6, 6.6)]);
+            SPARKLE.iter().for_each(|p| pen.fill(p));
         }
         Monitor => {
             pen.rrect(1.8, 2.5, 14.2, 11.0, 1.2);
@@ -740,6 +761,22 @@ fn keyframe_shapes(
 mod tests {
     use effectcraft_engine::keyframe::KeyHalf as H;
 
+    /// The Selection arrow (and the Speaker and Sparkle) are concave; filled as one polygon they
+    /// rendered as a broken fan. Each is drawn as convex pieces instead.
+    #[test]
+    fn concave_glyphs_are_filled_as_convex_pieces() {
+        for piece in super::CONCAVE.iter().flat_map(|g| g.iter()) {
+            let n = piece.len();
+            let turns: Vec<f32> = (0..n)
+                .map(|i| {
+                    let (a, b, c) = (piece[i], piece[(i + 1) % n], piece[(i + 2) % n]);
+                    (b.0 - a.0) * (c.1 - b.1) - (b.1 - a.1) * (c.0 - b.0)
+                })
+                .collect();
+            assert!(turns.iter().all(|t| *t < 0.0) || turns.iter().all(|t| *t > 0.0), "{piece:?} is not convex: {turns:?}");
+        }
+    }
+
     /// #284: keyframes have no dark border (overlapping keys looked messy): each half is filled
     /// and edged in the key's own colour.
     #[test]