diff --git a/test/functional/mempool_unbroadcast.py b/test/functional/mempool_unbroadcast.py
--- a/test/functional/mempool_unbroadcast.py
+++ b/test/functional/mempool_unbroadcast.py
@@ -16,6 +16,9 @@
     disconnect_nodes,
 )
 
+# 15 minutes in seconds
+MAX_INITIAL_BROADCAST_DELAY = 15 * 60
+
 
 class MempoolUnbroadcastTest(BitcoinTestFramework):
     def set_test_params(self):
@@ -75,7 +78,7 @@
 
         # fast forward into the future & ensure that the second node has the
         # txns
-        node.mockscheduler(15 * 60)  # 15 min in seconds
+        node.mockscheduler(MAX_INITIAL_BROADCAST_DELAY)
         self.sync_mempools(timeout=30)
         mempool = self.nodes[1].getrawmempool()
         assert rpc_tx_hsh in mempool
@@ -90,16 +93,18 @@
             "Add another connection & ensure transactions aren't broadcast again")
 
         conn = node.add_p2p_connection(P2PTxInvStore())
-        node.mockscheduler(15 * 60)
-        time.sleep(5)
+        node.mockscheduler(MAX_INITIAL_BROADCAST_DELAY)
+        # allow sufficient time for possibility of broadcast
+        time.sleep(2)
         assert_equal(len(conn.get_invs()), 0)
 
+        disconnect_nodes(node, self.nodes[1])
+        node.disconnect_p2ps()
+
     def test_txn_removal(self):
         self.log.info(
             "Test that transactions removed from mempool are removed from unbroadcast set")
         node = self.nodes[0]
-        disconnect_nodes(node, self.nodes[1])
-        node.disconnect_p2ps()
 
         # since the node doesn't have any connections, it will not receive
         # any GETDATAs & thus the transaction will remain in the unbroadcast