diff --git a/qa/pull-tester/rpc-tests.py b/qa/pull-tester/rpc-tests.py
index 778f8d8a77..58bd00fdfc 100755
--- a/qa/pull-tester/rpc-tests.py
+++ b/qa/pull-tester/rpc-tests.py
@@ -246,6 +246,10 @@ class RPCTestHandler:
         self.test_list = test_list
         self.flags = flags
         self.num_running = 0
+        # In case there is a graveyard of zombie bitcoinds, we can apply a
+        # pseudorandom offset to hopefully jump over them.
+        # (625 is PORT_RANGE/MAX_NODES)
+        self.portseed_offset = int(time.time() * 1000) % 625
         self.jobs = []
 
     def get_next(self):
@@ -253,7 +257,7 @@ class RPCTestHandler:
             # Add tests
             self.num_running += 1
             t = self.test_list.pop(0)
-            port_seed = ["--portseed=%s" % len(self.test_list)]
+            port_seed = ["--portseed={}".format(len(self.test_list) + self.portseed_offset)]
             log_stdout = tempfile.SpooledTemporaryFile(max_size=2**16)
             log_stderr = tempfile.SpooledTemporaryFile(max_size=2**16)
             self.jobs.append((t,