diff --git a/array_api_tests/hypothesis_helpers.py b/array_api_tests/hypothesis_helpers.py
index 4cbb1ab3..7045586c 100644
--- a/array_api_tests/hypothesis_helpers.py
+++ b/array_api_tests/hypothesis_helpers.py
@@ -4,7 +4,7 @@
 from operator import mul
 from typing import Any, List, NamedTuple, Optional, Sequence, Tuple, Union
 
-from hypothesis import assume
+from hypothesis import assume, note
 from hypothesis.strategies import (SearchStrategy, booleans, composite, floats,
                                    integers, just, lists, none, one_of,
                                    sampled_from, shared)
@@ -164,16 +164,39 @@ def matrix_shapes(draw, stack_shapes=shapes()):
                              elements=dict(allow_nan=False,
                                            allow_infinity=False))
 
-def mutually_broadcastable_shapes(
-    num_shapes: int, **kw
-) -> SearchStrategy[Tuple[Shape, ...]]:
-    return (
-        xps.mutually_broadcastable_shapes(num_shapes, **kw)
-        .map(lambda BS: BS.input_shapes)
-        .filter(lambda shapes: all(
-            prod(i for i in s if i > 0) < MAX_ARRAY_SIZE for s in shapes
-        ))
-    )
+@composite
+def mutually_broadcastable_shapes(draw, num_shapes, **kwargs):
+    # mutually_broadcastable_shapes() with the default inputs doesn't generate
+    # very interesting examples (see
+    # https://github.com/HypothesisWorks/hypothesis/issues/3170). It's very
+    # difficult to get it to do so by tweaking the max_* parameters, because
+    # making them too big leads to generating too large shapes and filtering
+    # too much. So instead, we trick it into generating more interesting
+    # examples by telling it to create shapes that broadcast against some base
+    # shape.
+    kwargs.setdefault('min_side', 0)
+    if 'base_shape' not in kwargs:
+        base_shape = draw(shapes(**kwargs))
+        kwargs['base_shape'] = base_shape
+
+    input_shapes, result_shape = draw(xps.mutually_broadcastable_shapes(num_shapes, **kwargs))
+
+    # result_shape is input_shapes broadcasted with base_shape, but base_shape
+    # itself is not part of input_shapes. We "really" want our base shape to
+    # be (). We are only using it here to trick mutually_broadcastable_shapes
+    # into giving more interesting examples.
+    final_result_shape = broadcast_shapes(*input_shapes)
+
+    # The broadcast compatible shapes can be bigger than the base shape. This
+    # is already somewhat limited by the mutually_broadcastable_shapes
+    # defaults, and pretty unlikely, but we filter again here just to be safe.
+    assume(prod(i for i in final_result_shape if i) < SQRT_MAX_ARRAY_SIZE)
+
+    # The hypothesis strategy would return this. We don't actually need the
+    # result shape in most cases (if we end up needing it, we can uncomment
+    # the below line).
+    # return BroadcastableShapes(input_shapes, final_result_shape)
+    return input_shapes
 
 two_mutually_broadcastable_shapes = mutually_broadcastable_shapes(2)