diff --git a/tests/test_gas_bomber_cooldowns.gd b/tests/test_gas_bomber_cooldowns.gd
index c80883e..ff1d616 100644
--- a/tests/test_gas_bomber_cooldowns.gd
+++ b/tests/test_gas_bomber_cooldowns.gd
@@ -44,8 +44,16 @@ func _process(delta: float) -> bool:
 	skill._process(0.0)
 	if first.is_ready() or not second.is_ready() or not skill.button.enabled:
 		return _fail("the first shot disabled more than its firing bomber")
-	if not first._filled_hull(fleet.ships[0].definition.hull_points, 0.0).is_empty() \
-			or first._filled_hull(fleet.ships[0].definition.hull_points, 0.5).size() < 3:
+	# _filled_hull returns a LIST of polygons: a notched hull fills as two
+	# separate puddles until the level rises past the notch, and the gas
+	# bomber's tail is exactly such a notch.
+	var hull: PackedVector2Array = fleet.ships[0].definition.hull_points
+	var empty: Array = first._filled_hull(hull, 0.0)
+	var half: Array = first._filled_hull(hull, 0.5)
+	var half_points: int = 0
+	for piece in half:
+		half_points += piece.size()
+	if not empty.is_empty() or half_points < 3:
 		return _fail("bomber cooldown did not produce an empty-to-filling hull")
 	if skill.projectiles.size() != 1:
 		return _fail("the first bomber did not launch exactly one projectile")
diff --git a/vessels/VesselCooldownFillComponent.gd b/vessels/VesselCooldownFillComponent.gd
index 8c009c1..f1c1b36 100644
--- a/vessels/VesselCooldownFillComponent.gd
+++ b/vessels/VesselCooldownFillComponent.gd
@@ -7,6 +7,14 @@ extends Node2D
 var cooldown_duration: float = 1.0
 var cooldown_left: float = 0.0
 
+# Two vertices this close together are the same vertex as far as the fill is
+# concerned - a hull is tens of units across, so this is well below anything
+# that could be a real edge.
+const WELD_DISTANCE: float = 0.01
+# Below this the fill is a sliver nobody can see, and drawing it is all cost
+# and no picture.
+const MIN_FILL_AREA: float = 0.5
+
 
 func setup() -> void:
 	show_behind_parent = true
@@ -37,30 +45,76 @@ func cooldown_progress() -> float:
 	return 1.0 - cooldown_left / maxf(cooldown_duration, 0.001)
 
 
-func _filled_hull(points: PackedVector2Array, progress: float) -> PackedVector2Array:
+# The part of the hull that is "filled up" at this progress, as a list of
+# polygons - plural, because a hull with a notch in it (the gas bomber's
+# tail, the distorder's waist) genuinely fills as two separate puddles
+# before the level rises past the notch.
+#
+# Geometry2D does the clipping. This used to walk the hull itself and cut
+# each edge against the fill line, which is Sutherland-Hodgman, and
+# Sutherland-Hodgman is only sound for a CONVEX subject: on a notched hull
+# it stitches the pieces back together with a zero-width bridge, and a
+# polygon with a zero-width bridge is not one Godot's triangulator will
+# accept. It said so, once per frame per cooling vessel, for as long as any
+# cooldown ran.
+func _filled_hull(points: PackedVector2Array, progress: float) -> Array:
 	if points.size() < 3 or progress <= 0.001:
-		return PackedVector2Array()
+		return []
 	if progress >= 0.999:
-		return points.duplicate()
+		return [points.duplicate()]
 	var top: float = INF
 	var bottom: float = -INF
+	var left: float = INF
+	var right: float = -INF
 	for point in points:
 		top = minf(top, point.y)
 		bottom = maxf(bottom, point.y)
+		left = minf(left, point.x)
+		right = maxf(right, point.x)
 	var fill_y: float = lerpf(bottom, top, clampf(progress, 0.0, 1.0))
-	var clipped := PackedVector2Array()
-	var previous: Vector2 = points[-1]
-	var previous_inside: bool = previous.y >= fill_y
-	for current in points:
-		var current_inside: bool = current.y >= fill_y
-		if current_inside != previous_inside:
-			var amount: float = (fill_y - previous.y) / (current.y - previous.y)
-			clipped.append(previous.lerp(current, amount))
-		if current_inside:
-			clipped.append(current)
-		previous = current
-		previous_inside = current_inside
-	return clipped
+	# Deliberately oversized sideways and downwards, so the box's own edges
+	# never coincide with the hull's and the only cut is the horizontal one.
+	var box := PackedVector2Array([
+		Vector2(left - 8.0, fill_y), Vector2(right + 8.0, fill_y),
+		Vector2(right + 8.0, bottom + 8.0), Vector2(left - 8.0, bottom + 8.0),
+	])
+	var pieces: Array = []
+	for piece in Geometry2D.intersect_polygons(points, box):
+		var drawable: PackedVector2Array = _drawable(piece)
+		if not drawable.is_empty():
+			pieces.append(drawable)
+	return pieces
+
+
+# Last guard before the renderer. The clipper is sound where the old walk
+# was not, but it can still hand back a vertex repeated at a corner, or a
+# sliver of a puddle at the very start of a fill - neither is worth drawing
+# and both are the shapes triangulation objects to.
+func _drawable(points: PackedVector2Array) -> PackedVector2Array:
+	var welded := PackedVector2Array()
+	for point in points:
+		if welded.is_empty() \
+				or welded[welded.size() - 1].distance_to(point) > WELD_DISTANCE:
+			welded.append(point)
+	# The polygon is implicitly closed, so the last point meeting the first is
+	# the same duplication seen from the other end.
+	while welded.size() >= 2 \
+			and welded[0].distance_to(welded[welded.size() - 1]) <= WELD_DISTANCE:
+		welded.remove_at(welded.size() - 1)
+	if welded.size() < 3 or _area(welded) < MIN_FILL_AREA:
+		return PackedVector2Array()
+	return welded
+
+
+# Shoelace, unsigned: the clip preserves the hull's winding, but which way a
+# hull winds is the definition's business and not worth depending on here.
+func _area(points: PackedVector2Array) -> float:
+	var total: float = 0.0
+	var previous: Vector2 = points[points.size() - 1]
+	for point in points:
+		total += previous.x * point.y - point.x * previous.y
+		previous = point
+	return absf(total) * 0.5
 
 
 func _draw() -> void:
@@ -75,9 +129,8 @@ func _draw() -> void:
 			ship.core_color, 0.75)
 		return
 	draw_colored_polygon(hull, Color(_cooling_color(), 0.58))
-	var filled: PackedVector2Array = _filled_hull(hull, cooldown_progress())
-	if filled.size() >= 3:
-		draw_colored_polygon(filled, Color(ready_color, 0.68))
+	for piece in _filled_hull(hull, cooldown_progress()):
+		draw_colored_polygon(piece, Color(ready_color, 0.68))
 
 
 func _ready_color() -> Color: return Color.WHITE