diff --git a/test/test_array.py b/test/test_array.py
index 381105bf8a3fc7cbeea70b658e863cb0efe6df99..b5e99273cf2d1313cd3c1506fa6d8a5912253a17 100644
--- a/test/test_array.py
+++ b/test/test_array.py
@@ -208,11 +208,13 @@ def test_vector_fill(ctx_factory):
 def test_zeros_large_array(ctx_factory):
     context = ctx_factory()
     queue = cl.CommandQueue(context)
+    dev = queue.device
 
-    if queue.device.address_bits == 64:
+    size = 2**28 + 1
+    if dev.address_bits == 64 and dev.max_mem_alloc_size >= 8 * size:
         # this shouldn't hang/cause errors
         # see https://github.com/inducer/pyopencl/issues/395
-        a_gpu = cl_array.zeros(queue, (2**28 + 1,), dtype="float64")
+        a_gpu = cl_array.zeros(queue, (size,), dtype="float64")
         # run a couple kernels to ensure no propagated runtime errors
         a_gpu[...] = 1.
         a_gpu = 2 * a_gpu - 3