diff --git a/array_api_tests/hypothesis_helpers.py b/array_api_tests/hypothesis_helpers.py
index 3033dac3..60c683c4 100644
--- a/array_api_tests/hypothesis_helpers.py
+++ b/array_api_tests/hypothesis_helpers.py
@@ -312,8 +312,8 @@ def positive_definite_matrices(draw, dtypes=xps.floating_dtypes()):
 @composite
 def invertible_matrices(draw, dtypes=xps.floating_dtypes(), stack_shapes=shapes()):
     # For now, just generate stacks of diagonal matrices.
-    n = draw(integers(0, SQRT_MAX_ARRAY_SIZE),)
     stack_shape = draw(stack_shapes)
+    n = draw(integers(0, SQRT_MAX_ARRAY_SIZE // max(math.prod(stack_shape), 1)),)
     dtype = draw(dtypes)
     elements = one_of(
         from_dtype(dtype, min_value=0.5, allow_nan=False, allow_infinity=False),
diff --git a/array_api_tests/test_linalg.py b/array_api_tests/test_linalg.py
index 465f54be..a20792ae 100644
--- a/array_api_tests/test_linalg.py
+++ b/array_api_tests/test_linalg.py
@@ -19,12 +19,14 @@
                                    data)
 from ndindex import iter_indices
 
+import math
 import itertools
+from typing import Tuple
 
 from .array_helpers import assert_exactly_equal, asarray
 from .hypothesis_helpers import (arrays, all_floating_dtypes, xps, shapes,
                                  kwargs, matrix_shapes, square_matrix_shapes,
-                                 symmetric_matrices,
+                                 symmetric_matrices, SearchStrategy,
                                  positive_definite_matrices, MAX_ARRAY_SIZE,
                                  invertible_matrices, two_mutual_arrays,
                                  mutually_promotable_dtypes, one_d_shapes,
@@ -35,6 +37,7 @@
 from . import dtype_helpers as dh
 from . import pytest_helpers as ph
 from . import shape_helpers as sh
+from .typing import Array
 
 from . import _array_module
 from . import _array_module as xp
@@ -589,7 +592,7 @@ def test_slogdet(x):
     # TODO: Test this when we have tests for floating-point values.
     # assert all(abs(linalg.det(x) - sign*exp(logabsdet)) < eps)
 
-def solve_args():
+def solve_args() -> Tuple[SearchStrategy[Array], SearchStrategy[Array]]:
     """
     Strategy for the x1 and x2 arguments to test_solve()
 
@@ -608,8 +611,9 @@ def solve_args():
 
     @composite
     def _x2_shapes(draw):
-        end = draw(integers(0, SQRT_MAX_ARRAY_SIZE))
-        return draw(stack_shapes)[1] + draw(x1).shape[-1:] + (end,)
+        base_shape = draw(stack_shapes)[1] + draw(x1).shape[-1:]
+        end = draw(integers(0, SQRT_MAX_ARRAY_SIZE // max(math.prod(base_shape), 1)))
+        return base_shape + (end,)
 
     x2_shapes = one_of(x1.map(lambda x: (x.shape[-1],)), _x2_shapes())
     x2 = arrays(shape=x2_shapes, dtype=mutual_dtypes.map(lambda pair: pair[1]))