diff --git a/coverage/data.py b/coverage/data.py
index f7469ed00..67b74d07c 100644
--- a/coverage/data.py
+++ b/coverage/data.py
@@ -12,7 +12,6 @@
 import random
 import re
 import socket
-import time
 
 from coverage import env
 from coverage.backward import iitems, string_class
@@ -666,9 +665,7 @@ def write(self, data, suffix=None):
                 with open(_TEST_NAME_FILE) as f:
                     test_name = f.read()
                 extra = "." + test_name
-            if env.WINDOWS:
-                time.sleep(0.001)           # Yuk: http://bugs.python.org/issue29085
-            dice = random.Random().randint(0, 999999)
+            dice = random.Random(os.urandom(8)).randint(0, 999999)
             suffix = "%s%s.%s.%06d" % (socket.gethostname(), extra, os.getpid(), dice)
 
         if suffix: