diff --git a/Lib/test/test_fcntl.py b/Lib/test/test_fcntl.py
index 58a57b5..2d800b2 100755
--- a/Lib/test/test_fcntl.py
+++ b/Lib/test/test_fcntl.py
@@ -25,7 +25,7 @@
                     'freebsd2', 'freebsd3', 'freebsd4', 'freebsd5',
                     'freebsd6', 'freebsd7',
                     'bsdos2', 'bsdos3', 'bsdos4',
-                    'openbsd', 'openbsd2', 'openbsd3'):
+                    'openbsd', 'openbsd2', 'openbsd3', 'openbsd4'):
     if struct.calcsize('l') == 8:
         off_t = 'l'
         pid_t = 'i'
diff --git a/Lib/test/test_tempfile.py b/Lib/test/test_tempfile.py
index aeaa77e..2047a63 100644
--- a/Lib/test/test_tempfile.py
+++ b/Lib/test/test_tempfile.py
@@ -27,7 +27,7 @@
 # number of files that can be opened at one time (see ulimit -n)
 if sys.platform == 'mac':
     TEST_FILES = 32
-elif sys.platform == 'openbsd3':
+elif sys.platform in ('openbsd3', 'openbsd4'):
     TEST_FILES = 48
 else:
     TEST_FILES = 100