diff --git a/src/OpenSSL/_util.py b/src/OpenSSL/_util.py
index cf8b888..cdcacc8 100644
--- a/src/OpenSSL/_util.py
+++ b/src/OpenSSL/_util.py
@@ -1,7 +1,7 @@
 import sys
 import warnings
 
-from six import PY3, binary_type, text_type
+from six import PY2, binary_type, text_type
 
 from cryptography.hazmat.bindings.openssl.binding import Binding
 
@@ -81,12 +81,12 @@
     """
     if not isinstance(s, (binary_type, text_type)):
         raise TypeError("%r is neither bytes nor unicode" % s)
-    if PY3:
-        if isinstance(s, binary_type):
-            return s.decode("utf-8")
-    else:
+    if PY2:
         if isinstance(s, text_type):
             return s.encode("utf-8")
+    else:
+        if isinstance(s, binary_type):
+            return s.decode("utf-8")
     return s
 
 
@@ -107,12 +107,12 @@
         raise TypeError("Path must be represented as bytes or unicode string")
 
 
-if PY3:
-    def byte_string(s):
-        return s.encode("charmap")
-else:
+if PY2:
     def byte_string(s):
         return s
+else:
+    def byte_string(s):
+        return s.encode("charmap")
 
 
 # A marker object to observe whether some optional arguments are passed any
diff --git a/tests/test_ssl.py b/tests/test_ssl.py
index 7704c72..6b9422c 100644
--- a/tests/test_ssl.py
+++ b/tests/test_ssl.py
@@ -25,7 +25,7 @@
 
 from pretend import raiser
 
-from six import PY3, text_type
+from six import PY2, text_type
 
 from cryptography import x509
 from cryptography.hazmat.backends import default_backend
@@ -101,7 +101,7 @@
 """
 
 
-skip_if_py3 = pytest.mark.skipif(PY3, reason="Python 2 only")
+skip_if_py3 = pytest.mark.skipif(not PY2, reason="Python 2 only")
 
 
 def socket_any_family():
@@ -2138,7 +2138,7 @@
         with pytest.raises(TypeError):
             conn.set_tlsext_host_name(b"with\0null")
 
-        if PY3:
+        if not PY2:
             # On Python 3.x, don't accidentally implicitly convert from text.
             with pytest.raises(TypeError):
                 conn.set_tlsext_host_name(b"example.com".decode("ascii"))
diff --git a/tests/util.py b/tests/util.py
index 4464379..65b905a 100644
--- a/tests/util.py
+++ b/tests/util.py
@@ -6,7 +6,7 @@
 U{Twisted<http://twistedmatrix.com/>}.
 """
 
-from six import PY3
+from six import PY2
 
 
 # This is the UTF-8 encoding of the SNOWMAN unicode code point.
@@ -152,7 +152,7 @@
 
 
 # The type name expected in warnings about using the wrong string type.
-if PY3:
-    WARNING_TYPE_EXPECTED = "str"
-else:
+if PY2:
     WARNING_TYPE_EXPECTED = "unicode"
+else:
+    WARNING_TYPE_EXPECTED = "str"