diff --git a/aephysics/shape/module.ae b/aephysics/shape/module.ae
index 89e0744..8b8ea94 100644
--- a/aephysics/shape/module.ae
+++ b/aephysics/shape/module.ae
@@ -326,7 +326,12 @@ shape_cast_shape(shape: *Shape, t: Transform, proxy: ShapeProxy, translation: Ve
     return output
 }
 
-overlap_shape(shape: *Shape, t: Transform, proxy: ShapeProxy) -> bool {
+overlap_shape(shape: *Shape, t: Transform, given: ShapeProxy) -> bool {
+    // The proxy's points copied first, as shape_cast_shape does: one made by
+    // make_shape_proxy for a sphere or capsule lives in the scratch the
+    // sphere's and capsule's overlaps write their own shape into, so GJK
+    // would have tested the shape against itself.
+    proxy = mesh.make_local_proxy(given, math.transform_identity(), local_buffer())
     kind = shape.kind
     if kind == SHAPE_CAPSULE { return capsule.overlap_capsule(shape.capsule, t, proxy) }
     if kind == SHAPE_COMPOUND { return compound.overlap_compound(shape.compound, t, proxy) }
diff --git a/tests/test_shape.ae b/tests/test_shape.ae
index 587d247..1875d01 100644
--- a/tests/test_shape.ae
+++ b/tests/test_shape.ae
@@ -558,6 +558,21 @@ test_far_origin() {
     free(offsets_block)
 }
 
+// A proxy made from one sphere tested against another far away: the
+// sphere's (and capsule's) overlap used to write its own shape into the
+// scratch the proxy's points live in, and so found its own copy touching.
+test_overlap_own_proxy() {
+    ball_a = shape.sphere_shape(manifold.sphere(math.vec3_zero(), 0.5), 1.0)
+    ball_b = shape.sphere_shape(manifold.sphere(math.vec3(10.0, 0.0, 0.0), 0.5), 1.0)
+    rod = shape.capsule_shape(manifold.capsule(math.vec3(10.0, 0.0, 0.0), math.vec3(10.0, 2.0, 0.0), 0.5), 1.0)
+    p = shape.make_shape_proxy(&ball_a)
+    ensure("own proxy: far sphere apart", shape.overlap_shape(&ball_b, math.transform_identity(), p) == false)
+    p = shape.make_shape_proxy(&ball_a)
+    ensure("own proxy: far capsule apart", shape.overlap_shape(&rod, math.transform_identity(), p) == false)
+    near = shape.sphere_shape(manifold.sphere(math.vec3(0.8, 0.0, 0.0), 0.5), 1.0)
+    p = shape.make_shape_proxy(&ball_a)
+    ensure("own proxy: near sphere touching", shape.overlap_shape(&near, math.transform_identity(), p))
+}
 test_dispatch() {
     origin = math.vec3(0.0 - 4.0, 0.0, 0.0)
     translation = math.vec3(8.0, 0.0, 0.0)
@@ -817,6 +832,7 @@ test_filters() {
 main() {
     before = basics.alloc_count()
     test_mass()
+    test_overlap_own_proxy()
     test_aabb()
     test_ray_cast_sphere()
     test_ray_cast_capsule()