diff --git a/Lib/imaplib.py b/Lib/imaplib.py
index c0334d8..00a17fb 100644
--- a/Lib/imaplib.py
+++ b/Lib/imaplib.py
@@ -360,10 +360,10 @@
 
                 data = authobject(response)
 
-        It will be called to process server continuation responses.
-        It should return data that will be encoded and sent to server.
-        It should return None if the client abort response '*' should
-        be sent instead.
+        It will be called to process server continuation responses; the
+        response argument it is passed will be a bytes.  It should return bytes
+        data that will be base64 encoded and sent to the server.  It should
+        return None if the client abort response '*' should be sent instead.
         """
         mech = mechanism.upper()
         # XXX: shouldn't this code be removed, not commented out?
@@ -546,7 +546,9 @@
     def _CRAM_MD5_AUTH(self, challenge):
         """ Authobject to use with CRAM-MD5 authentication. """
         import hmac
-        return self.user + " " + hmac.HMAC(self.password, challenge).hexdigest()
+        pwd = (self.password.encode('ASCII') if isinstance(self.password, str)
+                                             else self.password)
+        return self.user + " " + hmac.HMAC(pwd, challenge).hexdigest()
 
 
     def logout(self):
@@ -1288,14 +1290,16 @@
         #  so when it gets to the end of the 8-bit input
         #  there's no partial 6-bit output.
         #
-        oup = ''
+        oup = b''
+        if isinstance(inp, str):
+            inp = inp.encode('ASCII')
         while inp:
             if len(inp) > 48:
                 t = inp[:48]
                 inp = inp[48:]
             else:
                 t = inp
-                inp = ''
+                inp = b''
             e = binascii.b2a_base64(t)
             if e:
                 oup = oup + e[:-1]
@@ -1303,7 +1307,7 @@
 
     def decode(self, inp):
         if not inp:
-            return ''
+            return b''
         return binascii.a2b_base64(inp)