diff --git a/crates/effects/src/puppet/arap.rs b/crates/effects/src/puppet/arap.rs
index 9d46a978..19a87594 100644
--- a/crates/effects/src/puppet/arap.rs
+++ b/crates/effects/src/puppet/arap.rs
@@ -164,6 +164,12 @@ pub fn deform(rest: &[[f64; 2]], tris: &[[usize; 3]], weights: &[f64], h: &Handl
         t[1] /= h.fixed.len() as f64;
     }
     let x0: Vec<[f64; 2]> = rest.iter().map(|p| [p[0] + t[0], p[1] + t[1]]).collect();
+    // One pin and no edge targets: every rotation and scale about the pin costs nothing, and
+    // the regulariser that picks the translation is too weak to stop CG turning round-off
+    // into a visible rotation (#313). The translation is the exact solution.
+    if h.fixed.len() == 1 && h.edges.is_empty() {
+        return x0;
+    }
     let mut fixed = vec![false; n];
     for (i, _) in &h.fixed {
         fixed[*i] = true;
diff --git a/crates/effects/src/puppet/tests.rs b/crates/effects/src/puppet/tests.rs
index 066ac0c5..10426d46 100644
--- a/crates/effects/src/puppet/tests.rs
+++ b/crates/effects/src/puppet/tests.rs
@@ -306,3 +306,20 @@ fn groups_round_trip_serde() {
     assert_eq!(m[0].pins[1].kind, PinKind::Starch);
     assert_eq!(m[0].pins[0].position, [3.0, 4.0]);
 }
+
+#[test]
+fn single_pin_on_a_traced_solid_does_not_rotate_it() {
+    // #313: an 800×600 solid traced from its alpha, as the Puppet Pin tool builds it. One
+    // pin is not enough to rotate or scale the mesh, so it may only translate it.
+    let (w, h) = (800, 600);
+    let o = outline(&vec![1.0; w * h], w, h, 1.0, [0.0; 2], [400.0, 300.0], 3.0);
+    let m = triangulate(&o, &MeshOpts::default());
+    check_valid(&m);
+    for at in [[40.0, 40.0], [760.0, 30.0], [20.0, 580.0], [790.0, 590.0], [400.0, 300.0], [123.0, 456.0]] {
+        for t in [[0.0, 0.0], [35.0, -20.0]] {
+            let d = solve(&m, &[pin(PinKind::Position, at, [at[0] + t[0], at[1] + t[1]])], 2);
+            let err = d.iter().zip(&m.verts).map(|(a, b)| (a[0] - b[0] - t[0]).hypot(a[1] - b[1] - t[1])).fold(0.0, f64::max);
+            assert!(err < 1e-6, "pin at {at:?} moved by {t:?}: vertices off by up to {err} px");
+        }
+    }
+}
diff --git a/crates/engine/src/tests_paint.rs b/crates/engine/src/tests_paint.rs
index d6b5f9f1..4e05027a 100644
--- a/crates/engine/src/tests_paint.rs
+++ b/crates/engine/src/tests_paint.rs
@@ -186,6 +186,23 @@ fn puppet_pins_deform_and_undo() {
     assert_eq!(px(&s, 1.0, 100, 25), [0.0, 0.0, 1.0, 1.0]);
 }
 
+#[test]
+fn first_puppet_pin_leaves_the_layer_still() {
+    // #313: an 800×600 solid in a 1920×1080 comp turned about the first pin at these spots.
+    let mut s = Session::default();
+    s.execute("comp.new", json!({"name": "C", "width": 1920, "height": 1080, "duration": 2, "frameRate": 30})).unwrap();
+    let id = s.execute("layer.newSolid", json!({"width": 800, "height": 600, "color": [0, 0, 1]})).unwrap()["layer"].as_u64().unwrap();
+    let cid = s.active_comp_id().unwrap();
+    let before = s.render(cid, Tick::ZERO, RenderOpts::default());
+    for at in [[40, 40], [400, 300], [123, 456]] {
+        s.execute("puppet.addPin", json!({"layer": id, "position": at})).unwrap();
+        let after = s.render(cid, Tick::ZERO, RenderOpts::default());
+        let moved = after.data.iter().zip(&before.data).filter(|(a, b)| (0..4).any(|c| (a[c] - b[c]).abs() > 1e-3)).count();
+        assert_eq!(moved, 0, "pin at {at:?} changed {moved} pixels");
+        s.undo();
+    }
+}
+
 #[test]
 fn puppet_pin_kinds_and_mesh_options() {
     let (mut s, id) = setup();