diff --git a/paramiko/common.py b/paramiko/common.py
index 223aac1..e30df73 100644
--- a/paramiko/common.py
+++ b/paramiko/common.py
@@ -131,12 +131,12 @@ cr_byte = byte_chr(13)
 linefeed_byte = byte_chr(10)
 crlf = cr_byte + linefeed_byte
 
-if PY3:
-    cr_byte_value = 13
-    linefeed_byte_value = 10
-else:
+if PY2:
     cr_byte_value = cr_byte
     linefeed_byte_value = linefeed_byte
+else:
+    cr_byte_value = 13
+    linefeed_byte_value = 10
 
 
 def asbytes(s):
diff --git a/paramiko/file.py b/paramiko/file.py
index a0d94ef..c9f191a 100644
--- a/paramiko/file.py
+++ b/paramiko/file.py
@@ -92,8 +92,8 @@ class BufferedFile (object):
         self._wbuffer = BytesIO()
         return
 
-    if PY3:
-        def __next__(self):
+    if PY2:
+        def next(self):
             """
             Returns the next line from the input, or raises L{StopIteration} when
             EOF is hit.  Unlike python file objects, it's okay to mix calls to
@@ -109,7 +109,7 @@ class BufferedFile (object):
                 raise StopIteration
             return line
     else:
-        def next(self):
+        def __next__(self):
             """
             Returns the next line from the input, or raises L{StopIteration} when
             EOF is hit.  Unlike python file objects, it's okay to mix calls to
diff --git a/paramiko/py3compat.py b/paramiko/py3compat.py
index 0aad361..2228599 100644
--- a/paramiko/py3compat.py
+++ b/paramiko/py3compat.py
@@ -1,13 +1,101 @@
 import sys
 import base64
 
-__all__ = ['PY3', 'string_types', 'integer_types', 'text_type', 'bytes_types', 'bytes', 'long', 'input',
+__all__ = ['PY2', 'string_types', 'integer_types', 'text_type', 'bytes_types', 'bytes', 'long', 'input',
            'decodebytes', 'encodebytes', 'bytestring', 'byte_ord', 'byte_chr', 'byte_mask',
            'b', 'u', 'b2s', 'StringIO', 'BytesIO', 'is_callable', 'MAXSIZE', 'next']
 
-PY3 = sys.version_info[0] >= 3
+PY2 = sys.version_info[0] < 3
 
-if PY3:
+if PY2:
+    string_types = basestring
+    text_type = unicode
+    bytes_types = str
+    bytes = str
+    integer_types = (int, long)
+    long = long
+    input = raw_input
+    decodebytes = base64.decodestring
+    encodebytes = base64.encodestring
+
+
+    def bytestring(s):  # NOQA
+        if isinstance(s, unicode):
+            return s.encode('utf-8')
+        return s
+
+
+    byte_ord = ord  # NOQA
+    byte_chr = chr  # NOQA
+
+
+    def byte_mask(c, mask):
+        return chr(ord(c) & mask)
+
+
+    def b(s, encoding='utf8'):  # NOQA
+        """cast unicode or bytes to bytes"""
+        if isinstance(s, str):
+            return s
+        elif isinstance(s, unicode):
+            return s.encode(encoding)
+        else:
+            raise TypeError("Expected unicode or bytes, got %r" % s)
+
+
+    def u(s, encoding='utf8'):  # NOQA
+        """cast bytes or unicode to unicode"""
+        if isinstance(s, str):
+            return s.decode(encoding)
+        elif isinstance(s, unicode):
+            return s
+        else:
+            raise TypeError("Expected unicode or bytes, got %r" % s)
+
+
+    def b2s(s):
+        return s
+
+
+    try:
+        import cStringIO
+
+        StringIO = cStringIO.StringIO   # NOQA
+    except ImportError:
+        import StringIO
+
+        StringIO = StringIO.StringIO    # NOQA
+
+    BytesIO = StringIO
+
+
+    def is_callable(c):  # NOQA
+        return callable(c)
+
+
+    def get_next(c):  # NOQA
+        return c.next
+
+
+    def next(c):
+        return c.next()
+
+    # It's possible to have sizeof(long) != sizeof(Py_ssize_t).
+    class X(object):
+        def __len__(self):
+            return 1 << 31
+
+
+    try:
+        len(X())
+    except OverflowError:
+        # 32-bit
+        MAXSIZE = int((1 << 31) - 1)        # NOQA
+    else:
+        # 64-bit
+        MAXSIZE = int((1 << 63) - 1)        # NOQA
+    del X
+else:
     import collections
     import struct
     string_types = str
@@ -70,77 +158,3 @@ if PY3:
     next = next
 
     MAXSIZE = sys.maxsize       # NOQA
-else:
-    string_types = basestring
-    text_type = unicode
-    bytes_types = str
-    bytes = str
-    integer_types = (int, long)
-    long = long
-    input = raw_input
-    decodebytes = base64.decodestring
-    encodebytes = base64.encodestring
-
-    def bytestring(s):  # NOQA
-        if isinstance(s, unicode):
-            return s.encode('utf-8')
-        return s
-
-    byte_ord = ord  # NOQA
-    byte_chr = chr  # NOQA
-
-    def byte_mask(c, mask):
-        return chr(ord(c) & mask)
-
-    def b(s, encoding='utf8'):  # NOQA
-        """cast unicode or bytes to bytes"""
-        if isinstance(s, str):
-            return s
-        elif isinstance(s, unicode):
-            return s.encode(encoding)
-        else:
-            raise TypeError("Expected unicode or bytes, got %r" % s)
-
-    def u(s, encoding='utf8'):  # NOQA
-        """cast bytes or unicode to unicode"""
-        if isinstance(s, str):
-            return s.decode(encoding)
-        elif isinstance(s, unicode):
-            return s
-        else:
-            raise TypeError("Expected unicode or bytes, got %r" % s)
-
-    def b2s(s):
-        return s
-
-    try:
-        import cStringIO
-        StringIO = cStringIO.StringIO   # NOQA
-    except ImportError:
-        import StringIO
-        StringIO = StringIO.StringIO    # NOQA
-
-    BytesIO = StringIO
-
-    def is_callable(c):  # NOQA
-        return callable(c)
-
-    def get_next(c):  # NOQA
-        return c.next
-
-    def next(c):
-        return c.next()
-
-    # It's possible to have sizeof(long) != sizeof(Py_ssize_t).
-    class X(object):
-        def __len__(self):
-            return 1 << 31
-    try:
-        len(X())
-    except OverflowError:
-        # 32-bit
-        MAXSIZE = int((1 << 31) - 1)        # NOQA
-    else:
-        # 64-bit
-        MAXSIZE = int((1 << 63) - 1)        # NOQA
-    del X
diff --git a/paramiko/util.py b/paramiko/util.py
index 51fa6d6..71fc467 100644
--- a/paramiko/util.py
+++ b/paramiko/util.py
@@ -63,8 +63,8 @@ def inflate_long(s, always_positive=False):
         out -= (long(1) << (8 * len(s)))
     return out
 
-deflate_zero = 0 if PY3 else zero_byte
-deflate_ff = 0xff if PY3 else max_byte
+deflate_zero = zero_byte if PY2 else 0
+deflate_ff = max_byte if PY2 else 0xff
 
 def deflate_long(n, add_sign_padding=True):
     "turns a long-int into a normalized byte string (adapted from Crypto.Util.number)"
diff --git a/test.py b/test.py
index c8ac6bc..bd966d1 100755
--- a/test.py
+++ b/test.py
@@ -29,7 +29,7 @@ import unittest
 from optparse import OptionParser
 import paramiko
 import threading
-from paramiko.py3compat import PY3
+from paramiko.py3compat import PY2
 
 sys.path.append('tests')
 
@@ -149,10 +149,10 @@ def main():
     # TODO: make that not a problem, jeez
     for thread in threading.enumerate():
         if thread is not threading.currentThread():
-            if PY3:
-                thread._stop()
-            else:
+            if PY2:
                 thread._Thread__stop()
+            else:
+                thread._stop()
     # Exit correctly
     if not result.wasSuccessful():
         sys.exit(1)
diff --git a/tests/test_pkey.py b/tests/test_pkey.py
index f854946..19c5c69 100644
--- a/tests/test_pkey.py
+++ b/tests/test_pkey.py
@@ -23,7 +23,7 @@ Some unit tests for public/private key objects.
 from binascii import hexlify, unhexlify
 import unittest
 from paramiko import RSAKey, DSSKey, ECDSAKey, Message, util
-from paramiko.common import rng, StringIO, byte_chr, b, PY3, bytes
+from paramiko.common import rng, StringIO, byte_chr, b, bytes
 from tests.util import test_path
 
 # from openssh's ssh-keygen
diff --git a/tests/test_sftp.py b/tests/test_sftp.py
index b84b3fd..4a41258 100755
--- a/tests/test_sftp.py
+++ b/tests/test_sftp.py
@@ -72,8 +72,8 @@ FOLDER = os.environ.get('TEST_FOLDER', 'temp-testing000')
 sftp = None
 tc = None
 g_big_file_test = True
-unicode_folder = eval(compile(r"'\u00fcnic\u00f8de'" if PY3 else r"u'\u00fcnic\u00f8de'", 'test_sftp.py', 'eval'))
-utf8_folder = eval(compile(r"b'/\xc3\xbcnic\xc3\xb8\x64\x65'" if PY3 else r"'/\xc3\xbcnic\xc3\xb8\x64\x65'", 'test_sftp.py', 'eval'))
+unicode_folder = eval(compile(r"u'\u00fcnic\u00f8de'" if PY2 else r"'\u00fcnic\u00f8de'", 'test_sftp.py', 'eval'))
+utf8_folder = eval(compile(r"'/\xc3\xbcnic\xc3\xb8\x64\x65'" if PY2 else r"b'/\xc3\xbcnic\xc3\xb8\x64\x65'", 'test_sftp.py', 'eval'))
 
 def get_sftp():
     global sftp