diff --git a/test/test_clrandom.py b/test/test_clrandom.py
index 2846e24c97e1c4c0356420dfa35a1278e615a77f..0cd572d0208cf092eef57648c273f40a88b29c39 100644
--- a/test/test_clrandom.py
+++ b/test/test_clrandom.py
@@ -31,6 +31,7 @@ import pyopencl.clrandom as clrandom
 from pyopencl.tools import (  # noqa
         pytest_generate_tests_for_pyopencl
         as pytest_generate_tests)
+from pyopencl.characterize import has_double_support
 
 try:
     import faulthandler
@@ -59,6 +60,8 @@ def make_ranlux_generator(cl_ctx):
     cltypes.float4])
 def test_clrandom_dtypes(ctx_factory, rng_class, dtype):
     cl_ctx = ctx_factory()
+    if dtype == np.float64 and not has_double_support(cl_ctx.devices[0]):
+        pytest.skip("double precision not supported on this device")
     rng = rng_class(cl_ctx)
 
     size = 10
diff --git a/test/test_wrapper.py b/test/test_wrapper.py
index 118eee740c26640c36acd5834842d67c465c54f1..a17866fa77110f4d1b232898ca46c76f54ec4a83 100644
--- a/test/test_wrapper.py
+++ b/test/test_wrapper.py
@@ -953,6 +953,7 @@ def test_coarse_grain_svm(ctx_factory):
     dev = ctx.devices[0]
 
     has_svm = (ctx._get_cl_version() >= (2, 0) and
+                ctx.devices[0]._get_cl_version() >= (2, 0) and
                 cl.get_cl_header_version() >= (2, 0))
 
     if dev.platform.name == "Portable Computing Language":