diff --git a/test/functional/p2p_leak.py b/test/functional/p2p_leak.py
--- a/test/functional/p2p_leak.py
+++ b/test/functional/p2p_leak.py
@@ -139,7 +139,11 @@
         no_version_idlenode = self.nodes[0].add_p2p_connection(
             CNodeNoVersionIdle(), send_version=False, wait_for_verack=False)
         no_verack_idlenode = self.nodes[0].add_p2p_connection(
-            CNodeNoVerackIdle())
+            CNodeNoVerackIdle(), wait_for_verack=False)
+
+        # Wait until we got the verack in response to the version. Though, don't wait for the other node to receive the
+        # verack, since we never sent one
+        no_verack_idlenode.wait_for_verack()
 
         wait_until(lambda: no_version_bannode.ever_connected,
                    timeout=10, lock=mininode_lock)
diff --git a/test/functional/p2p_timeouts.py b/test/functional/p2p_timeouts.py
--- a/test/functional/p2p_timeouts.py
+++ b/test/functional/p2p_timeouts.py
@@ -43,12 +43,17 @@
 
     def run_test(self):
         # Setup the p2p connections
-        no_verack_node = self.nodes[0].add_p2p_connection(TestP2PConn())
+        no_verack_node = self.nodes[0].add_p2p_connection(
+            TestP2PConn(), wait_for_verack=False)
         no_version_node = self.nodes[0].add_p2p_connection(
             TestP2PConn(), send_version=False, wait_for_verack=False)
         no_send_node = self.nodes[0].add_p2p_connection(
             TestP2PConn(), send_version=False, wait_for_verack=False)
 
+        # Wait until we got the verack in response to the version. Though, don't wait for the other node to receive the
+        # verack, since we never sent one
+        no_verack_node.wait_for_verack()
+
         sleep(1)
 
         assert no_verack_node.is_connected
diff --git a/test/functional/test_framework/test_node.py b/test/functional/test_framework/test_node.py
--- a/test/functional/test_framework/test_node.py
+++ b/test/functional/test_framework/test_node.py
@@ -484,7 +484,20 @@
         p2p_conn.peer_connect(**kwargs, net=self.chain)()
         self.p2ps.append(p2p_conn)
         if wait_for_verack:
+            # Wait for the node to send us the version and verack
             p2p_conn.wait_for_verack()
+            # At this point we have sent our version message and received the version and verack, however the full node
+            # has not yet received the verack from us (in reply to their version). So, the connection is not yet fully
+            # established (fSuccessfullyConnected).
+            #
+            # This shouldn't lead to any issues when sending messages, since the verack will be in-flight before the
+            # message we send. However, it might lead to races where we are expecting to receive a message. E.g. a
+            # transaction that will be added to the mempool as soon as we return here.
+            #
+            # So syncing here is redundant when we only want to send a message, but the cost is low (a few milliseconds)
+            # in comparision to the upside of making tests less fragile and
+            # unexpected intermittent errors less likely.
+            p2p_conn.sync_with_ping()
 
         return p2p_conn