diff --git a/src/wormhole/test/test_transit.py b/src/wormhole/test/test_transit.py
index dee0e63..62848b4 100644
--- a/src/wormhole/test/test_transit.py
+++ b/src/wormhole/test/test_transit.py
@@ -1374,6 +1374,56 @@ class Transit(unittest.TestCase):
         self._waiters[0].callback("winner")
         self.assertEqual(results, ["winner"])
 
+    @inlineCallbacks
+    def test_priorities(self):
+        clock = task.Clock()
+        s = transit.TransitSender("", reactor=clock, no_listen=True)
+        s.set_transit_key(b"key")
+        hints = yield s.get_connection_hints()
+        del hints
+        s.add_connection_hints([
+            {"type": "relay-v1",
+             "hints": [{"type": "direct-tcp-v1",
+                        "hostname": "relay", "port": 1234}]},
+            {"type": "direct-tcp-v1",
+             "hostname": "direct", "port": 1234},
+            {"type": "relay-v1",
+             "hints": [{"type": "direct-tcp-v1", "priority": 2.0,
+                        "hostname": "relay2", "port": 1234},
+                       {"type": "direct-tcp-v1", "priority": 3.0,
+                        "hostname": "relay3", "port": 1234}]},
+            {"type": "relay-v1",
+             "hints": [{"type": "direct-tcp-v1", "priority": 2.0,
+                        "hostname": "relay4", "port": 1234}]},
+            ])
+        s._endpoint_from_hint_obj = self._endpoint_from_hint_obj
+        s._start_connector = self._start_connector
+
+        d = s.connect()
+        results = []
+        d.addBoth(results.append)
+        self.assertEqual(results, [])
+        # direct connector should be used first, then the priority=3.0 relay,
+        # then the two 2.0 relays, then the (default) 0.0 relay
+
+        self.assertEqual(self._connectors, ["direct"])
+
+        clock.advance(s.RELAY_DELAY + 1.0)
+        self.assertEqual(self._connectors, ["direct", "relay3"])
+
+        clock.advance(s.RELAY_DELAY)
+        self.assertIn(self._connectors,
+                      (["direct", "relay3", "relay2", "relay4"],
+                       ["direct", "relay3", "relay4", "relay2"]))
+
+        clock.advance(s.RELAY_DELAY)
+        self.assertIn(self._connectors,
+                      (["direct", "relay3", "relay2", "relay4", "relay"],
+                       ["direct", "relay3", "relay4", "relay2", "relay"]))
+
+        self._waiters[0].callback("winner")
+        self.assertEqual(results, ["winner"])
+
     @inlineCallbacks
     def test_no_direct_hints(self):
         clock = task.Clock()
diff --git a/src/wormhole/transit.py b/src/wormhole/transit.py
index 20b8d88..4aa5972 100644
--- a/src/wormhole/transit.py
+++ b/src/wormhole/transit.py
@@ -821,8 +821,17 @@ class Common:
         # resolve quickly. Many direct hints will be to unused local-network
         # IP addresses, which won't answer, and would take the full TCP
         # timeout (30s or more) to fail.
+
+        prioritized_relays = {}
         for rh in self._our_relay_hints:
             for hint_obj in rh.hints:
+                priority = hint_obj.priority
+                if priority not in prioritized_relays:
+                    prioritized_relays[priority] = set()
+                prioritized_relays[priority].add(hint_obj)
+
+        for priority in sorted(prioritized_relays, reverse=True):
+            for hint_obj in prioritized_relays[priority]:
                 ep = self._endpoint_from_hint_obj(hint_obj)
                 if not ep:
                     continue
@@ -831,6 +840,7 @@ class Common:
                                     self._start_connector, ep, description,
                                     is_relay=True)
                 contenders.append(d)
+            relay_delay += self.RELAY_DELAY
 
         if not contenders:
             raise TransitError("No contenders for connection")