diff --git a/test/functional/p2p_inv_download.py b/test/functional/p2p_inv_download.py
--- a/test/functional/p2p_inv_download.py
+++ b/test/functional/p2p_inv_download.py
@@ -107,6 +107,9 @@
 # Python test constants
 NUM_INBOUND = 10
 
+# Common network parameters
+UNCONDITIONAL_RELAY_DELAY = 2 * 60
+
 
 def skip(context):
     def decorator(test):
@@ -162,7 +165,7 @@
         self.log.info("All outstanding peers received a getdata")
 
     @skip(PROOF_TEST_CONTEXT)
-    def test_inv_block(self, context):
+    def test_inv_tx(self, context):
         self.log.info("Generate a transaction on node 0")
         tx = self.nodes[0].createrawtransaction(
             inputs=[{
@@ -188,20 +191,30 @@
         self.log.info("Put the tx in node 0's mempool")
         self.nodes[0].sendrawtransaction(tx)
 
+        # node1 is an inbound peer for node0, so the tx relay is delayed by a
+        # duration calculated using a poisson's law with a 5s average time.
+        # In order to make sure the inv is sent we move the time 2 minutes
+        # forward, which has the added side effect that the tx can be
+        # unconditionally requested.
+        with self.nodes[1].assert_debug_log([f"got inv: tx {txid:064x}  new peer=0"]):
+            self.nodes[0].setmocktime(
+                int(time.time()) + UNCONDITIONAL_RELAY_DELAY)
+
         # Since node 1 is connected outbound to an honest peer (node 0), it
-        # should get the tx within a timeout. (Assuming that node 0
-        # announced the tx within the timeout)
+        # should get the tx within a timeout.
         # The timeout is the sum of
         # * the worst case until the tx is first requested from an inbound
         #   peer, plus
         # * the first time it is re-requested from the outbound peer, plus
         # * 2 seconds to avoid races
         assert self.nodes[1].getpeerinfo()[0]['inbound'] is False
-        timeout = 2 + context.constants.inbound_peer_delay + \
+        max_delay = context.constants.inbound_peer_delay + \
             context.constants.getdata_interval
+        margin = 2
         self.log.info(
-            "Tx should be received at node 1 after {} seconds".format(timeout))
-        self.sync_mempools(timeout=timeout)
+            "Tx should be received at node 1 after {} seconds".format(max_delay + margin))
+        self.nodes[1].setmocktime(int(time.time()) + max_delay)
+        self.sync_mempools(timeout=margin)
 
     def test_in_flight_max(self, context):
         max_getdata_in_flight = context.constants.max_getdata_in_flight
@@ -459,7 +472,7 @@
 
             # Run each test against new bitcoind instances, as setting mocktimes has long-term effects on when
             # the next trickle relay event happens.
-            for test in [self.test_in_flight_max, self.test_inv_block,
+            for test in [self.test_in_flight_max, self.test_inv_tx,
                          self.test_data_requests, self.test_orphan_download, self.test_request_invalid_once]:
                 self.stop_nodes()
                 self.start_nodes()