diff --git a/array_api_strict/tests/test_elementwise_functions.py b/array_api_strict/tests/test_elementwise_functions.py
index 90994f3..fa3405a 100644
--- a/array_api_strict/tests/test_elementwise_functions.py
+++ b/array_api_strict/tests/test_elementwise_functions.py
@@ -9,6 +9,11 @@
     _boolean_dtypes,
     _floating_dtypes,
     _integer_dtypes,
+    int8,
+    int16,
+    int32,
+    int64,
+    uint64,
 )
 from .._flags import set_array_api_strict_flags
 
@@ -115,6 +120,17 @@ def _array_vals():
             func = getattr(_elementwise_functions, func_name)
             if nargs(func) == 2:
                 for y in _array_vals():
+                    # Disallow dtypes that aren't type promotable
+                    if (x.dtype == uint64 and y.dtype in [int8, int16, int32, int64]
+                         or y.dtype == uint64 and x.dtype in [int8, int16, int32, int64]
+                         or x.dtype in _integer_dtypes and y.dtype not in _integer_dtypes
+                         or y.dtype in _integer_dtypes and x.dtype not in _integer_dtypes
+                         or x.dtype in _boolean_dtypes and y.dtype not in _boolean_dtypes
+                         or y.dtype in _boolean_dtypes and x.dtype not in _boolean_dtypes
+                         or x.dtype in _floating_dtypes and y.dtype not in _floating_dtypes
+                         or y.dtype in _floating_dtypes and x.dtype not in _floating_dtypes
+                         ):
+                        assert_raises(TypeError, lambda: func(x, y))
                     if x.dtype not in dtypes or y.dtype not in dtypes:
                         assert_raises(TypeError, lambda: func(x, y))
             else: