diff --git a/Changelog.md b/Changelog.md
--- a/Changelog.md
+++ b/Changelog.md
@@ -1,5 +1,16 @@
 # Changelog for net-mqtt
 
+## 0.5.1.0
+
+The QuickCheck Arbitrary instances are exported in a module now,
+allowing programs to generate useful tests other implementations of
+mqtt.  I've been using this package to test a C implementation.
+
+Also, don't allow 3.1.1 to generate a password without a username.
+That's kind of a weird limitation in the older protocol I'm not sure
+anyone's run into, but the spec says not to encode things on the wire
+that way, so it's useful for interop testing.
+
 ## 0.5.0.2
 
 With a few attempts to misuse the library, I found some places where
diff --git a/net-mqtt.cabal b/net-mqtt.cabal
--- a/net-mqtt.cabal
+++ b/net-mqtt.cabal
@@ -4,10 +4,10 @@
 --
 -- see: https://github.com/sol/hpack
 --
--- hash: 3c221d190f39c9b883915e0e17701983e95297762972cda53caf5f87b53856c1
+-- hash: ae5e3dfe2f39a8729bd34aa29df254e2761a1537f932d801ec64c90aee241705
 
 name:           net-mqtt
-version:        0.5.0.2
+version:        0.5.1.0
 synopsis:       An MQTT Protocol Implementation.
 description:    Please see the README on GitHub at <https://github.com/dustin/mqtt-hs#readme>
 category:       Network
@@ -29,6 +29,7 @@
 
 library
   exposed-modules:
+      Network.MQTT.Arbitrary
       Network.MQTT.Client
       Network.MQTT.Topic
       Network.MQTT.Types
@@ -38,7 +39,8 @@
       src
   ghc-options: -Wall
   build-depends:
-      async >=2.2.1 && <2.3
+      QuickCheck
+    , async >=2.2.1 && <2.3
     , attoparsec >=0.13.2 && <0.14
     , attoparsec-binary >=0.2 && <1.0
     , base >=4.7 && <5
@@ -61,7 +63,8 @@
       app
   ghc-options: -Wall -threaded -rtsopts -with-rtsopts=-N
   build-depends:
-      async >=2.2.1 && <2.3
+      QuickCheck
+    , async >=2.2.1 && <2.3
     , attoparsec >=0.13.2 && <0.14
     , attoparsec-binary >=0.2 && <1.0
     , base >=4.7 && <5
diff --git a/src/Network/MQTT/Arbitrary.hs b/src/Network/MQTT/Arbitrary.hs
new file mode 100644
--- /dev/null
+++ b/src/Network/MQTT/Arbitrary.hs
@@ -0,0 +1,209 @@
+{-|
+Module       : Network.MQTT.Arbitrary
+Description  : Arbitrary instances for QuickCheck.
+Copyright    : (c) Dustin Sallings, 2019
+License      : BSD3
+Maintainer   : dustin@spy.net
+Stability    : experimental
+
+Arbitrary instances for QuickCheck.
+-}
+
+{-# LANGUAGE OverloadedStrings #-}
+{-# LANGUAGE RecordWildCards   #-}
+{-# OPTIONS_GHC -Wno-orphans #-}
+
+module Network.MQTT.Arbitrary (
+  SizeT(..),
+  v311mask
+  ) where
+
+import           Control.Applicative   (liftA2)
+import qualified Data.ByteString.Char8 as BC
+import qualified Data.ByteString.Lazy  as L
+import           Network.MQTT.Types    as MT
+import           Test.QuickCheck       as QC
+
+
+
+-- | Arbitrary type fitting variable integers.
+newtype SizeT = SizeT Int deriving(Eq, Show)
+
+instance Arbitrary SizeT where
+  arbitrary = SizeT <$> oneof [ choose (0, 127),
+                                choose (128, 16383),
+                                choose (16384, 2097151),
+                                choose (2097152, 268435455)]
+
+instance Arbitrary LastWill where
+  arbitrary = LastWill <$> arbitrary <*> arbitrary <*> astr <*> astr <*> arbitrary
+
+instance Arbitrary ProtocolLevel where arbitrary = arbitraryBoundedEnum
+
+instance Arbitrary ConnectRequest where
+  arbitrary = do
+    _username <- mastr
+    _password <- mastr
+    _connID <- astr
+    _cleanSession <- arbitrary
+    _keepAlive <- arbitrary
+    _lastWill <- arbitrary
+    _properties <- arbitrary
+
+    pure ConnectRequest{..}
+
+mastr :: Gen (Maybe L.ByteString)
+mastr = fmap (L.fromStrict . BC.pack . getUnicodeString) <$> arbitrary
+
+astr :: Gen L.ByteString
+astr = L.fromStrict . BC.pack . getUnicodeString <$> arbitrary
+
+instance Arbitrary QoS where
+  arbitrary = arbitraryBoundedEnum
+
+instance Arbitrary ConnACKFlags where
+  arbitrary = ConnACKFlags <$> arbitrary <*> arbitrary <*> arbitrary
+  shrink (ConnACKFlags b c pl)
+    | null pl = []
+    | otherwise = ConnACKFlags b c <$> shrink pl
+
+instance Arbitrary PublishRequest where
+  arbitrary = do
+    _pubDup <- arbitrary
+    _pubQoS <- arbitrary
+    _pubRetain <- arbitrary
+    _pubTopic <- astr
+    _pubPktID <- if _pubQoS == QoS0 then pure 0 else arbitrary
+    _pubBody <- astr
+    _pubProps <- arbitrary
+    pure PublishRequest{..}
+
+instance Arbitrary PubACK where
+  arbitrary = PubACK <$> arbitrary <*> arbitrary <*> arbitrary
+
+instance Arbitrary PubREL where
+  arbitrary = PubREL <$> arbitrary <*> arbitrary <*> arbitrary
+
+instance Arbitrary PubREC where
+  arbitrary = PubREC <$> arbitrary <*> arbitrary <*> arbitrary
+
+instance Arbitrary PubCOMP where
+  arbitrary = PubCOMP <$> arbitrary <*> arbitrary <*> arbitrary
+
+instance Arbitrary SubscribeRequest where
+  arbitrary = arbitrary >>= \pid -> choose (1,11) >>= \n -> SubscribeRequest pid <$> vectorOf n sub <*> arbitrary
+    where sub = liftA2 (,) astr arbitrary
+
+  shrink (SubscribeRequest w s p) =
+    if length s < 2 then []
+    else [SubscribeRequest w (take 1 s) p' | p' <- shrinkList (:[]) p, length p > 1]
+
+instance Arbitrary SubOptions where
+  arbitrary = SubOptions <$> arbitraryBoundedEnum <*> arbitrary <*> arbitrary <*> arbitrary
+
+instance Arbitrary SubErr where arbitrary = arbitraryBoundedEnum
+
+instance Arbitrary SubscribeResponse where
+  arbitrary = arbitrary >>= \pid -> choose (1,11) >>= \n -> SubscribeResponse pid <$> vectorOf n arbitrary <*> arbitrary
+
+  shrink (SubscribeResponse pid l props)
+    | length l == 1 = []
+    | otherwise = [SubscribeResponse pid sl props | sl <- shrinkList (:[]) l, not (null sl)]
+
+instance Arbitrary UnsubscribeRequest where
+  arbitrary = arbitrary >>= \pid -> choose (1,11) >>= \n -> UnsubscribeRequest pid <$> vectorOf n astr <*> arbitrary
+  shrink (UnsubscribeRequest p l props)
+    | length l == 1 = []
+    | otherwise = [UnsubscribeRequest p sl props | sl <- shrinkList (:[]) l, not (null sl)]
+
+instance Arbitrary UnsubStatus where arbitrary = arbitraryBoundedEnum
+
+instance Arbitrary UnsubscribeResponse where
+  arbitrary = UnsubscribeResponse <$> arbitrary <*> arbitrary <*> arbitrary
+
+instance Arbitrary MT.Property where
+  arbitrary = oneof [
+    PropPayloadFormatIndicator <$> arbitrary,
+    PropMessageExpiryInterval <$> arbitrary,
+    PropMessageExpiryInterval <$> arbitrary,
+    PropContentType <$> astr,
+    PropResponseTopic <$> astr,
+    PropCorrelationData <$> astr,
+    PropSubscriptionIdentifier <$> arbitrary `suchThat` (>= 0),
+    PropSessionExpiryInterval <$> arbitrary,
+    PropAssignedClientIdentifier <$> astr,
+    PropServerKeepAlive <$> arbitrary,
+    PropAuthenticationMethod <$> astr,
+    PropAuthenticationData <$> astr,
+    PropRequestProblemInformation <$> arbitrary,
+    PropWillDelayInterval <$> arbitrary,
+    PropRequestResponseInformation <$> arbitrary,
+    PropResponseInformation <$> astr,
+    PropServerReference <$> astr,
+    PropReasonString <$> astr,
+    PropReceiveMaximum <$> arbitrary,
+    PropTopicAliasMaximum <$> arbitrary,
+    PropTopicAlias <$> arbitrary,
+    PropMaximumQoS <$> arbitrary,
+    PropRetainAvailable <$> arbitrary,
+    PropUserProperty <$> astr <*> astr,
+    PropMaximumPacketSize <$> arbitrary,
+    PropWildcardSubscriptionAvailable <$> arbitrary,
+    PropSubscriptionIdentifierAvailable <$> arbitrary,
+    PropSharedSubscriptionAvailable <$> arbitrary
+    ]
+
+instance Arbitrary AuthRequest where
+  arbitrary = AuthRequest <$> arbitrary <*> arbitrary
+
+instance Arbitrary ConnACKRC where arbitrary = arbitraryBoundedEnum
+
+instance Arbitrary DiscoReason where arbitrary = arbitraryBoundedEnum
+
+instance Arbitrary DisconnectRequest where
+  arbitrary = DisconnectRequest <$> arbitrary <*> arbitrary
+
+instance Arbitrary MQTTPkt where
+  arbitrary = oneof [
+    ConnPkt <$> arbitrary,
+    ConnACKPkt <$> arbitrary,
+    PublishPkt <$> arbitrary,
+    PubACKPkt <$> arbitrary,
+    PubRELPkt <$> arbitrary,
+    PubRECPkt <$> arbitrary,
+    PubCOMPPkt <$> arbitrary,
+    SubscribePkt <$> arbitrary,
+    SubACKPkt <$> arbitrary,
+    UnsubscribePkt <$> arbitrary,
+    UnsubACKPkt <$> arbitrary,
+    pure PingPkt, pure PongPkt,
+    DisconnectPkt <$> arbitrary,
+    AuthPkt <$> arbitrary
+    ]
+  shrink (SubACKPkt x)      = SubACKPkt <$> shrink x
+  shrink (ConnACKPkt x)     = ConnACKPkt <$> shrink x
+  shrink (UnsubscribePkt x) = UnsubscribePkt <$> shrink x
+  shrink (SubscribePkt x)   = SubscribePkt <$> shrink x
+  shrink _                  = []
+
+-- | v311mask strips all the v5 specific bits from an MQTTPkt.
+v311mask :: MQTTPkt -> MQTTPkt
+v311mask (ConnPkt c@ConnectRequest{..}) = ConnPkt (c{_properties=mempty,
+                                                     _password=mpw _username _password,
+                                                     _lastWill=cl <$> _lastWill})
+  where cl lw = lw{_willProps=mempty}
+        mpw Nothing _ = Nothing
+        mpw _ p       = p
+v311mask (ConnACKPkt (ConnACKFlags a b _)) = ConnACKPkt (ConnACKFlags a b mempty)
+v311mask (SubscribePkt (SubscribeRequest p s _)) = SubscribePkt (SubscribeRequest p c mempty)
+  where c = map (\(k,SubOptions{..}) -> (k,subOptions{_subQoS=_subQoS})) s
+v311mask (SubACKPkt (SubscribeResponse p s _)) = SubACKPkt (SubscribeResponse p s mempty)
+v311mask (UnsubscribePkt (UnsubscribeRequest p l _)) = UnsubscribePkt (UnsubscribeRequest p l mempty)
+v311mask (UnsubACKPkt (UnsubscribeResponse p _ _)) = UnsubACKPkt (UnsubscribeResponse p mempty mempty)
+v311mask (PublishPkt req) = PublishPkt req{_pubProps=mempty}
+v311mask (DisconnectPkt _) = DisconnectPkt (DisconnectRequest DiscoNormalDisconnection mempty)
+v311mask (PubACKPkt (PubACK x _ _)) = PubACKPkt (PubACK x 0 mempty)
+v311mask (PubRECPkt (PubREC x _ _)) = PubRECPkt (PubREC x 0 mempty)
+v311mask (PubRELPkt (PubREL x _ _)) = PubRELPkt (PubREL x 0 mempty)
+v311mask (PubCOMPPkt (PubCOMP x _ _)) = PubCOMPPkt (PubCOMP x 0 mempty)
+v311mask x = x
diff --git a/src/Network/MQTT/Types.hs b/src/Network/MQTT/Types.hs
--- a/src/Network/MQTT/Types.hs
+++ b/src/Network/MQTT/Types.hs
@@ -319,7 +319,7 @@
                         <> toByteString prot _connID
                         <> lwt _lastWill
                         <> perhaps _username
-                        <> perhaps _password
+                        <> if isJust _username then perhaps _password else ""
 
       val Protocol50 = "\NUL\EOTMQTT\ENQ" -- MQTT + Protocol50
                        <> BL.singleton connBits
@@ -333,7 +333,7 @@
       connBits = hasu .|. hasp .|. willBits .|. clean
         where
           hasu = boolBit (isJust _username) ≪ 7
-          hasp = boolBit (isJust _password) ≪ 6
+          hasp = boolBit ((prot == Protocol50 || isJust _username) && isJust _password) ≪ 6
           clean = boolBit _cleanSession ≪ 1
           willBits = case _lastWill of
                        Nothing -> 0
diff --git a/test/Spec.hs b/test/Spec.hs
--- a/test/Spec.hs
+++ b/test/Spec.hs
@@ -1,30 +1,18 @@
 {-# LANGUAGE OverloadedStrings #-}
 {-# LANGUAGE RecordWildCards   #-}
 
-import           Control.Applicative             (liftA2)
 import           Control.Monad                   (mapM_)
 import qualified Data.Attoparsec.ByteString.Lazy as A
-import qualified Data.ByteString                 as B
-import qualified Data.ByteString.Char8           as BC
 import qualified Data.ByteString.Lazy            as L
 import           Data.Word                       (Word8)
-import           Numeric                         (showHex)
+import           Network.MQTT.Arbitrary
+import           Network.MQTT.Topic
+import           Network.MQTT.Types              as MT
 import           Test.QuickCheck                 as QC
 import           Test.Tasty
 import           Test.Tasty.HUnit
 import           Test.Tasty.QuickCheck           as QC
 
-import           Network.MQTT.Topic
-import           Network.MQTT.Types              as MT
-
-newtype SizeT = SizeT Int deriving(Eq, Show)
-
-instance Arbitrary SizeT where
-  arbitrary = SizeT <$> oneof [ choose (0, 127),
-                                choose (128, 16383),
-                                choose (16384, 2097151),
-                                choose (2097152, 268435455)]
-
 prop_rtLengthParser :: SizeT -> QC.Property
 prop_rtLengthParser (SizeT x) =
   label (show (length e) <> "B") $
@@ -49,157 +37,6 @@
         f@A.Fail{}    -> assertFailure (show f)
         (A.Done _ x') -> assertEqual (show s) x x'
 
-instance Arbitrary LastWill where
-  arbitrary = LastWill <$> arbitrary <*> arbitrary <*> astr <*> astr <*> arbitrary
-
-instance Arbitrary ProtocolLevel where arbitrary = arbitraryBoundedEnum
-
-instance Arbitrary ConnectRequest where
-  arbitrary = do
-    _username <- mastr
-    _password <- mastr
-    _connID <- astr
-    _cleanSession <- arbitrary
-    _keepAlive <- arbitrary
-    _lastWill <- arbitrary
-    _properties <- arbitrary
-
-    pure ConnectRequest{..}
-
-mastr :: Gen (Maybe L.ByteString)
-mastr = fmap (L.fromStrict . BC.pack . getUnicodeString) <$> arbitrary
-
-astr :: Gen L.ByteString
-astr = L.fromStrict . BC.pack . getUnicodeString <$> arbitrary
-
-instance Arbitrary QoS where
-  arbitrary = arbitraryBoundedEnum
-
-instance Arbitrary ConnACKFlags where
-  arbitrary = ConnACKFlags <$> arbitrary <*> arbitrary <*> arbitrary
-  shrink (ConnACKFlags b c pl)
-    | null pl = []
-    | otherwise = ConnACKFlags b c <$> shrink pl
-
-instance Arbitrary PublishRequest where
-  arbitrary = do
-    _pubDup <- arbitrary
-    _pubQoS <- arbitrary
-    _pubRetain <- arbitrary
-    _pubTopic <- astr
-    _pubPktID <- if _pubQoS == QoS0 then pure 0 else arbitrary
-    _pubBody <- astr
-    _pubProps <- arbitrary
-    pure PublishRequest{..}
-
-instance Arbitrary PubACK where
-  arbitrary = PubACK <$> arbitrary <*> arbitrary <*> arbitrary
-
-instance Arbitrary PubREL where
-  arbitrary = PubREL <$> arbitrary <*> arbitrary <*> arbitrary
-
-instance Arbitrary PubREC where
-  arbitrary = PubREC <$> arbitrary <*> arbitrary <*> arbitrary
-
-instance Arbitrary PubCOMP where
-  arbitrary = PubCOMP <$> arbitrary <*> arbitrary <*> arbitrary
-
-instance Arbitrary SubscribeRequest where
-  arbitrary = arbitrary >>= \pid -> choose (1,11) >>= \n -> SubscribeRequest pid <$> vectorOf n sub <*> arbitrary
-    where sub = liftA2 (,) astr arbitrary
-
-  shrink (SubscribeRequest w s p) =
-    if length s < 2 then []
-    else [SubscribeRequest w (take 1 s) p' | p' <- shrinkList (:[]) p, length p > 1]
-
-instance Arbitrary SubOptions where
-  arbitrary = SubOptions <$> arbitraryBoundedEnum <*> arbitrary <*> arbitrary <*> arbitrary
-
-instance Arbitrary SubErr where arbitrary = arbitraryBoundedEnum
-
-instance Arbitrary SubscribeResponse where
-  arbitrary = arbitrary >>= \pid -> choose (1,11) >>= \n -> SubscribeResponse pid <$> vectorOf n arbitrary <*> arbitrary
-
-  shrink (SubscribeResponse pid l props)
-    | length l == 1 = []
-    | otherwise = [SubscribeResponse pid sl props | sl <- shrinkList (:[]) l, not (null sl)]
-
-instance Arbitrary UnsubscribeRequest where
-  arbitrary = arbitrary >>= \pid -> choose (1,11) >>= \n -> UnsubscribeRequest pid <$> vectorOf n astr <*> arbitrary
-  shrink (UnsubscribeRequest p l props)
-    | length l == 1 = []
-    | otherwise = [UnsubscribeRequest p sl props | sl <- shrinkList (:[]) l, not (null sl)]
-
-instance Arbitrary UnsubStatus where arbitrary = arbitraryBoundedEnum
-
-instance Arbitrary UnsubscribeResponse where
-  arbitrary = UnsubscribeResponse <$> arbitrary <*> arbitrary <*> arbitrary
-
-instance Arbitrary MT.Property where
-  arbitrary = oneof [
-    PropPayloadFormatIndicator <$> arbitrary,
-    PropMessageExpiryInterval <$> arbitrary,
-    PropMessageExpiryInterval <$> arbitrary,
-    PropContentType <$> astr,
-    PropResponseTopic <$> astr,
-    PropCorrelationData <$> astr,
-    PropSubscriptionIdentifier <$> arbitrary `suchThat` (>= 0),
-    PropSessionExpiryInterval <$> arbitrary,
-    PropAssignedClientIdentifier <$> astr,
-    PropServerKeepAlive <$> arbitrary,
-    PropAuthenticationMethod <$> astr,
-    PropAuthenticationData <$> astr,
-    PropRequestProblemInformation <$> arbitrary,
-    PropWillDelayInterval <$> arbitrary,
-    PropRequestResponseInformation <$> arbitrary,
-    PropResponseInformation <$> astr,
-    PropServerReference <$> astr,
-    PropReasonString <$> astr,
-    PropReceiveMaximum <$> arbitrary,
-    PropTopicAliasMaximum <$> arbitrary,
-    PropTopicAlias <$> arbitrary,
-    PropMaximumQoS <$> arbitrary,
-    PropRetainAvailable <$> arbitrary,
-    PropUserProperty <$> astr <*> astr,
-    PropMaximumPacketSize <$> arbitrary,
-    PropWildcardSubscriptionAvailable <$> arbitrary,
-    PropSubscriptionIdentifierAvailable <$> arbitrary,
-    PropSharedSubscriptionAvailable <$> arbitrary
-    ]
-
-instance Arbitrary AuthRequest where
-  arbitrary = AuthRequest <$> arbitrary <*> arbitrary
-
-instance Arbitrary ConnACKRC where arbitrary = arbitraryBoundedEnum
-
-instance Arbitrary DiscoReason where arbitrary = arbitraryBoundedEnum
-
-instance Arbitrary DisconnectRequest where
-  arbitrary = DisconnectRequest <$> arbitrary <*> arbitrary
-
-instance Arbitrary MQTTPkt where
-  arbitrary = oneof [
-    ConnPkt <$> arbitrary,
-    ConnACKPkt <$> arbitrary,
-    PublishPkt <$> arbitrary,
-    PubACKPkt <$> arbitrary,
-    PubRELPkt <$> arbitrary,
-    PubRECPkt <$> arbitrary,
-    PubCOMPPkt <$> arbitrary,
-    SubscribePkt <$> arbitrary,
-    SubACKPkt <$> arbitrary,
-    UnsubscribePkt <$> arbitrary,
-    UnsubACKPkt <$> arbitrary,
-    pure PingPkt, pure PongPkt,
-    DisconnectPkt <$> arbitrary,
-    AuthPkt <$> arbitrary
-    ]
-  shrink (SubACKPkt x)      = SubACKPkt <$> shrink x
-  shrink (ConnACKPkt x)     = ConnACKPkt <$> shrink x
-  shrink (UnsubscribePkt x) = UnsubscribePkt <$> shrink x
-  shrink (SubscribePkt x)   = SubscribePkt <$> shrink x
-  shrink _                  = []
-
 prop_PacketRT50 :: MQTTPkt -> QC.Property
 prop_PacketRT50 p = label (lab p) $ case A.parse (parsePacket Protocol50) (toByteString Protocol50 p) of
                                          A.Fail{}     -> False
@@ -216,22 +53,6 @@
 
   where
     lab x = let (s,_) = break (== ' ') . show $ x in s
-    v311mask :: MQTTPkt -> MQTTPkt
-    v311mask (ConnPkt c) = ConnPkt (c{_properties=mempty, _lastWill=cl <$> _lastWill c})
-      where cl lw = lw{_willProps=mempty}
-    v311mask (ConnACKPkt (ConnACKFlags a b _)) = ConnACKPkt (ConnACKFlags a b mempty)
-    v311mask (SubscribePkt (SubscribeRequest p s _)) = SubscribePkt (SubscribeRequest p c mempty)
-      where c = map (\(k,SubOptions{..}) -> (k,subOptions{_subQoS=_subQoS})) s
-    v311mask (SubACKPkt (SubscribeResponse p s _)) = SubACKPkt (SubscribeResponse p s mempty)
-    v311mask (UnsubscribePkt (UnsubscribeRequest p l _)) = UnsubscribePkt (UnsubscribeRequest p l mempty)
-    v311mask (UnsubACKPkt (UnsubscribeResponse p _ _)) = UnsubACKPkt (UnsubscribeResponse p mempty mempty)
-    v311mask (PublishPkt req) = PublishPkt req{_pubProps=mempty}
-    v311mask (DisconnectPkt _) = DisconnectPkt (DisconnectRequest DiscoNormalDisconnection mempty)
-    v311mask (PubACKPkt (PubACK x _ _)) = PubACKPkt (PubACK x 0 mempty)
-    v311mask (PubRECPkt (PubREC x _ _)) = PubRECPkt (PubREC x 0 mempty)
-    v311mask (PubRELPkt (PubREL x _ _)) = PubRELPkt (PubREL x 0 mempty)
-    v311mask (PubCOMPPkt (PubCOMP x _ _)) = PubCOMPPkt (PubCOMP x 0 mempty)
-    v311mask x = x
 
     available (AuthPkt _) = False
     available _           = True