diff --git a/MySQLdb/compat.py b/MySQLdb/compat.py
new file mode 100644
index 0000000..4d84afe
--- /dev/null
+++ b/MySQLdb/compat.py
@@ -0,0 +1,8 @@
+import sys
+
+if sys.version_info[0] == 3:
+    unicode = str
+    unichr = chr
+else:
+    unicode = unicode
+    unichr = unichr
diff --git a/MySQLdb/connections.py b/MySQLdb/connections.py
index 13e55c4..a7adc99 100644
--- a/MySQLdb/connections.py
+++ b/MySQLdb/connections.py
@@ -7,10 +7,11 @@ override Connection.default_cursor with a non-standard Cursor class.
 
 """
 from MySQLdb import cursors
+from MySQLdb.compat import unicode
 from _mysql_exceptions import Warning, Error, InterfaceError, DataError, \
      DatabaseError, OperationalError, IntegrityError, InternalError, \
      NotSupportedError, ProgrammingError
-import types, _mysql
+import _mysql
 import re
 
 
@@ -233,8 +234,8 @@ class Connection(_mysql.connection):
             self.converter[FIELD_TYPE.VARCHAR].append((None, string_decoder))
             self.converter[FIELD_TYPE.BLOB].append((None, string_decoder))
 
-        self.encoders[types.StringType] = string_literal
-        self.encoders[types.UnicodeType] = unicode_literal
+        self.encoders[bytes] = string_literal
+        self.encoders[unicode] = unicode_literal
         self._transactional = self.server_capabilities & CLIENT.TRANSACTIONS
         if self._transactional:
             if autocommit is not None:
diff --git a/MySQLdb/cursors.py b/MySQLdb/cursors.py
index b45ddaf..c19f256 100644
--- a/MySQLdb/cursors.py
+++ b/MySQLdb/cursors.py
@@ -7,13 +7,8 @@ default, MySQLdb uses the Cursor class.
 
 import re
 import sys
-try:
-    from types import ListType, TupleType, UnicodeType
-except ImportError:
-    # Python 3
-    ListType = list
-    TupleType = tuple
-    UnicodeType = str
+
+from MySQLdb.compat import unicode
 
 restr = r"""
     \s
@@ -305,7 +300,7 @@ class BaseCursor(object):
         q = "CALL %s(%s)" % (procname,
                              ','.join(['@_%s_%d' % (procname, i)
                                        for i in range(len(args))]))
-        if type(q) is UnicodeType:
+        if isinstance(q, unicode):
             q = q.encode(db.unicode_literal.charset)
         self._query(q)
         self._executed = q
diff --git a/metadata.cfg b/metadata.cfg
index 49841c1..ea31c01 100644
--- a/metadata.cfg
+++ b/metadata.cfg
@@ -44,6 +44,7 @@ classifiers:
         Topic :: Database :: Database Engines/Servers
 py_modules:
         _mysql_exceptions
+        MySQLdb.compat
         MySQLdb.converters
         MySQLdb.connections
         MySQLdb.cursors
diff --git a/tests/capabilities.py b/tests/capabilities.py
index 076361c..5b122cb 100644
--- a/tests/capabilities.py
+++ b/tests/capabilities.py
@@ -10,6 +10,8 @@ import array
 import unittest
 from configdb import connection_factory
 
+from MySQLdb.compat import unichr
+
 
 class DatabaseTest(unittest.TestCase):