diff --git a/OpenSSL/test/test_rand.py b/OpenSSL/test/test_rand.py
index 3d5c290..f86e4bf 100644
--- a/OpenSSL/test/test_rand.py
+++ b/OpenSSL/test/test_rand.py
@@ -205,8 +205,7 @@
         Random data can be saved and loaded to files with paths specified as
         bytes.
         """
-        path = self.mktemp()
-        path += NON_ASCII.encode(sys.getfilesystemencoding())
+        path = self.mktemp(suffix=NON_ASCII)
         self._read_write_test(path)
 
 
@@ -215,7 +214,7 @@
         Random data can be saved and loaded to files with paths specified as
         unicode.
         """
-        path = self.mktemp().decode('utf-8') + NON_ASCII
+        path = self.mktemp(suffix=NON_ASCII).decode('utf-8')
         self._read_write_test(path)
 
 
diff --git a/OpenSSL/test/test_ssl.py b/OpenSSL/test/test_ssl.py
index bb1c9ae..808b8a6 100644
--- a/OpenSSL/test/test_ssl.py
+++ b/OpenSSL/test/test_ssl.py
@@ -436,7 +436,7 @@
         instance giving the file name to ``Context.use_privatekey_file``.
         """
         self._use_privatekey_file_test(
-            self.mktemp() + NON_ASCII.encode(getfilesystemencoding()),
+            self.mktemp(suffix=NON_ASCII),
             FILETYPE_PEM,
         )
 
@@ -447,7 +447,7 @@
         instance giving the file name to ``Context.use_privatekey_file``.
         """
         self._use_privatekey_file_test(
-            self.mktemp().decode(getfilesystemencoding()) + NON_ASCII,
+            self.mktemp(suffix=NON_ASCII).decode(getfilesystemencoding()),
             FILETYPE_PEM,
         )
 
@@ -545,7 +545,7 @@
         ``bytes`` filename) which will be used to identify connections created
         using the context.
         """
-        filename = self.mktemp() + NON_ASCII.encode(getfilesystemencoding())
+        filename = self.mktemp(suffix=NON_ASCII)
         self._use_certificate_file_test(filename)
 
 
@@ -555,7 +555,9 @@
         ``bytes`` filename) which will be used to identify connections created
         using the context.
         """
-        filename = self.mktemp().decode(getfilesystemencoding()) + NON_ASCII
+        filename = self.mktemp(
+            suffix=NON_ASCII
+        ).decode(getfilesystemencoding())
         self._use_certificate_file_test(filename)
 
 
@@ -990,7 +992,7 @@
         ``bytes`` instance and uses the certificates within for verification
         purposes.
         """
-        cafile = self.mktemp() + NON_ASCII.encode(getfilesystemencoding())
+        cafile = self.mktemp(suffix=NON_ASCII)
         self._load_verify_cafile(cafile)
 
 
@@ -1001,7 +1003,7 @@
         purposes.
         """
         self._load_verify_cafile(
-            self.mktemp().decode(getfilesystemencoding()) + NON_ASCII
+            self.mktemp(suffix=NON_ASCII).decode(getfilesystemencoding())
         )
 
 
@@ -1041,7 +1043,7 @@
         purposes.
         """
         self._load_verify_directory_locations_capath(
-            self.mktemp() + NON_ASCII.encode(getfilesystemencoding())
+            self.mktemp(suffix=NON_ASCII)
         )
 
 
@@ -1052,7 +1054,7 @@
         purposes.
         """
         self._load_verify_directory_locations_capath(
-            self.mktemp().decode(getfilesystemencoding()) + NON_ASCII
+            self.mktemp(suffix=NON_ASCII)
         )
 
 
@@ -1287,7 +1289,7 @@
         construct and verify a trust chain.
         """
         self._use_certificate_chain_file_test(
-            self.mktemp() + NON_ASCII.encode(getfilesystemencoding())
+            self.mktemp(suffix=NON_ASCII)
         )
 
 
@@ -1298,7 +1300,7 @@
         to construct and verify a trust chain.
         """
         self._use_certificate_chain_file_test(
-            self.mktemp().decode(getfilesystemencoding()) + NON_ASCII
+            self.mktemp(suffix=NON_ASCII)
         )
 
 
@@ -1395,7 +1397,7 @@
         specified file (given as ``bytes``).
         """
         self._load_tmp_dh_test(
-            self.mktemp() + NON_ASCII.encode(getfilesystemencoding()),
+            self.mktemp(suffix=NON_ASCII)
         )
 
 
@@ -1405,7 +1407,7 @@
         specified file (given as ``unicode``).
         """
         self._load_tmp_dh_test(
-            self.mktemp().decode(getfilesystemencoding()) + NON_ASCII,
+            self.mktemp(suffix=NON_ASCII).decode(getfilesystemencoding())
         )
 
 
diff --git a/OpenSSL/test/util.py b/OpenSSL/test/util.py
index 12e5eb8..c26a57a 100644
--- a/OpenSSL/test/util.py
+++ b/OpenSSL/test/util.py
@@ -296,13 +296,13 @@
 
 
     _temporaryFiles = None
-    def mktemp(self):
+    def mktemp(self, suffix=""):
         """
         Pathetic substitute for twisted.trial.unittest.TestCase.mktemp.
         """
         if self._temporaryFiles is None:
             self._temporaryFiles = []
-        temp = b(mktemp(dir="."))
+        temp = mktemp(suffix=suffix, dir=".").encode("utf-8")
         self._temporaryFiles.append(temp)
         return temp