diff --git a/autoarray/structures/triangles/array.py b/autoarray/structures/triangles/array.py
index 0ed7cd4e6..1e92897f8 100644
--- a/autoarray/structures/triangles/array.py
+++ b/autoarray/structures/triangles/array.py
@@ -10,7 +10,7 @@
 from autoarray.structures.triangles.shape import Shape
 from autoarray.structures.triangles.shape import _barycentric_contains
 
-MAX_CONTAINING_SIZE = 15
+MAX_CONTAINING_SIZE = 20
 
 # Private A/B switch for the step-0 containment route (point-source CPU phase 4b,
 # PyAutoArray#579). It only affects `ArrayTriangles` built by
diff --git a/test_autoarray/structures/triangles/test_coordinate_jax.py b/test_autoarray/structures/triangles/test_coordinate_jax.py
index 292e831c7..2824d10aa 100644
--- a/test_autoarray/structures/triangles/test_coordinate_jax.py
+++ b/test_autoarray/structures/triangles/test_coordinate_jax.py
@@ -586,3 +586,61 @@ def containing(vertices, point):
     assert all(size < 3 * n * 2 for size in gathered), (
         f"step-0 containment gathers {gathered} elements; the triangle array is {3 * n * 2}"
     )
+
+
+# A 16- and a 17-sheet fold: the static lattice's vertices are traced through z -> z**k (z = x + iy),
+# so a source point at |w| = 1 has k preimages on the unit circle, each in the interior of exactly one
+# traced triangle -- a k-member containing set with no boundary ties. The PointSolver's uncapped
+# step-0 maximum on 200 prior draws was 17 (prior draw 12, point-source CPU phase 4c,
+# PyAutoArray#583), which the old cap of 15 truncated silently.
+FOLD_LIMITS = dict(y_min=-1.3, y_max=1.3, x_min=-1.3, x_max=1.3, scale=0.05)
+
+
+@pytest.mark.parametrize("sheets", [16, 17])
+def test__containing_set_above_the_old_cap_is_not_truncated(sheets):
+    """
+    Under ``jit``, a 16- or 17-triangle containing set keeps every member at the default
+    `MAX_CONTAINING_SIZE` (20), padded to ``(20,)``; the old cap of 15, passed explicitly, drops
+    some. Red at ``MAX_CONTAINING_SIZE = 15``.
+    """
+    lattice = _static_lattice(FOLD_LIMITS)
+    z = lattice.vertices[:, 1] + 1j * lattice.vertices[:, 0]
+    w = z**sheets
+    traced = jnp.stack([w.imag, w.real], axis=1)
+    point = (float(np.sin(0.3)), float(np.cos(0.3)))
+
+    uncapped = np.flatnonzero(
+        np.asarray(Point(*point).mask(lattice.with_vertices(traced).triangles))
+    )
+    assert len(uncapped) == sheets
+
+    def containing(vertices, max_containing_size=None):
+        kwargs = (
+            {}
+            if max_containing_size is None
+            else {"max_containing_size": max_containing_size}
+        )
+        triangles = triangles_array.ArrayTriangles(
+            indices=lattice.indices,
+            vertices=vertices,
+            step0_layout=lattice.step0_layout,
+            **kwargs,
+        )
+        return triangles.containing_indices(Point(*point))
+
+    assert lattice.with_vertices(traced).max_containing_size == MAX_CONTAINING_SIZE
+
+    kept = np.asarray(jax.jit(containing)(traced))
+    assert np.array_equal(np.sort(kept[kept >= 0]), uncapped)
+    assert kept.shape == (20,)
+
+    kept_via_lattice = np.asarray(
+        jax.jit(lambda v: lattice.with_vertices(v).containing_indices(Point(*point)))(
+            traced
+        )
+    )
+    assert np.array_equal(kept_via_lattice, kept)
+
+    old_cap = np.asarray(jax.jit(lambda v: containing(v, 15))(traced))
+    assert old_cap.shape == (15,)
+    assert np.sum(old_cap >= 0) == 15 < sheets