diff --git a/array_api_tests/dtype_helpers.py b/array_api_tests/dtype_helpers.py
index 6ff8d49c..4729d8f9 100644
--- a/array_api_tests/dtype_helpers.py
+++ b/array_api_tests/dtype_helpers.py
@@ -322,7 +322,7 @@ def accumulation_result_dtype(x_dtype, dtype_kwarg):
     default_float = xp.asarray(float()).dtype
     if default_float not in real_float_dtypes:
         warn(f"inferred default float is {default_float!r}, which is not a float")
-    if api_version > "2021.12":
+    if api_version > "2021.12" and ({'complex64', 'complex128'} - set(skip_dtypes)):
         default_complex = xp.asarray(complex()).dtype
         if default_complex not in complex_dtypes:
             warn(
diff --git a/array_api_tests/hypothesis_helpers.py b/array_api_tests/hypothesis_helpers.py
index cc70c13d..54255cb4 100644
--- a/array_api_tests/hypothesis_helpers.py
+++ b/array_api_tests/hypothesis_helpers.py
@@ -186,11 +186,11 @@ def oneway_broadcastable_shapes(draw) -> OnewayBroadcastableShapes:
 real_floating_dtypes = sampled_from(dh.real_float_dtypes)
 numeric_dtypes = sampled_from(dh.numeric_dtypes)
 # Note: this always returns complex dtypes, even if api_version < 2022.12
-complex_dtypes = sampled_from(dh.complex_dtypes)
+complex_dtypes: SearchStrategy[Any] | None = sampled_from(dh.complex_dtypes) if dh.complex_dtypes else None
 
 def all_floating_dtypes() -> SearchStrategy[DataType]:
     strat = floating_dtypes
-    if api_version >= "2022.12":
+    if api_version >= "2022.12" and complex_dtypes is not None:
         strat |= complex_dtypes
     return strat