diff --git a/xCAT-test/blackboxtest/src/blackboxtest_lib/dhcp.py b/xCAT-test/blackboxtest/src/blackboxtest_lib/dhcp.py
index 55102f3c7..d6fa1120d 100644
--- a/xCAT-test/blackboxtest/src/blackboxtest_lib/dhcp.py
+++ b/xCAT-test/blackboxtest/src/blackboxtest_lib/dhcp.py
@@ -228,8 +228,9 @@ class Wire(object):
     def send(self, frame):
         self.socket.send(frame)
 
-    def collect(self, session, deadline):
-        """Every reply to this session's xid until `deadline`.
+    def collect(self, session, deadline, stop=()):
+        """Every reply to this session's xid until `deadline`, or until a
+        reply of a type in `stop` arrives.
 
         A reply of an unexpected type is kept, so a NAK where an ACK was
         wanted is reported as a NAK rather than as a timeout.
@@ -237,7 +238,8 @@ class Wire(object):
         found = []
         while True:
             remaining = deadline - time.monotonic()
-            if remaining <= 0 or not select.select([self.socket], [], [], remaining)[0]:
+            if remaining <= 0 or any(r.fields["msgtype"] in stop for r in found) \
+                    or not select.select([self.socket], [], [], remaining)[0]:
                 return found
             frame = self.socket.recv(2048)
             if frame is None:
@@ -293,7 +295,8 @@ def run_step(step, session, context, timeout, retries):
         sent = describe(step, session, trans, context)
         session.wire.send(build_frame(step, session, trans, context,
                                       session.wire.scapy))
-        replies = session.wire.collect(session, time.monotonic() + timeout)
+        replies = session.wire.collect(session, time.monotonic() + timeout,
+                                       stop_on(step, wanted))
         if any(r.fields["msgtype"] in wanted for r in replies) \
                 or (replies and not wanted):
             break
@@ -328,6 +331,18 @@ def run_step(step, session, context, timeout, retries):
     return chosen, extras, sent
 
 
+def stop_on(step, wanted):
+    """The reply types that end a step's listening window early.
+
+    A step that counts `offers` must hear every server, so it listens for the
+    whole timeout. So does `expect = none`, where silence is the result.
+    """
+    if any("offers" in (a.target, a.value)
+           for a in step.assertions):
+        return frozenset()
+    return wanted
+
+
 def distinct_servers(replies):
     """One reply per answering server.
 
diff --git a/xCAT-test/blackboxtest/tests/test_dhcp.py b/xCAT-test/blackboxtest/tests/test_dhcp.py
index 4ddd4c86a..05ef66bfa 100644
--- a/xCAT-test/blackboxtest/tests/test_dhcp.py
+++ b/xCAT-test/blackboxtest/tests/test_dhcp.py
@@ -164,7 +164,8 @@ class FakeWire(object):
     def send(self, frame):
         self.sent += 1
 
-    def collect(self, session, deadline):
+    def collect(self, session, deadline, stop=()):
+        self.stop = stop
         return self.answers.pop(0) if self.answers else []
 
     def close(self):
@@ -239,6 +240,16 @@ class StepLoop(unittest.TestCase):
             self.assertEqual(extras["met"], met)
             self.assertEqual(session.state, dhcp.INIT)
 
+    def test_a_step_stops_listening_once_its_reply_arrived(self):
+        # Unless it counts the servers that answered, or proves silence.
+        cases = (("", {"OFFER"}), ("assert =\n    offers == 1\n", set()),
+                 ("expect = none\n", set()))
+        for extra, stop in cases:
+            step, = self.step("[step d]\ntype = discover\n" + extra)
+            session = dhcp.Session(FakeWire([reply("OFFER")]))
+            dhcp.run_step(step, session, subst.Context(), 0.1, 1)
+            self.assertEqual(set(session.wire.stop), stop, extra)
+
     def test_a_step_mac_replaces_the_random_one(self):
         step, = self.step("[step d]\ntype = discover\nmac = 02-00-00-00-00-AA\n")
         session = dhcp.Session(FakeWire())