diff --git a/test/functional/p2p_filter.py b/test/functional/p2p_filter.py
--- a/test/functional/p2p_filter.py
+++ b/test/functional/p2p_filter.py
@@ -261,11 +261,6 @@
         filter_peer_without_nrelay = self.nodes[0].add_p2p_connection(
             P2PBloomFilter(), send_version=False, wait_for_verack=False)
         # Send version with fRelay=False
-        filter_peer_without_nrelay.wait_until(
-            lambda: filter_peer_without_nrelay.is_connected,
-            timeout=10,
-            check_connected=False,
-        )
         version_without_fRelay = msg_version()
         version_without_fRelay.nRelay = 0
         filter_peer_without_nrelay.send_message(version_without_fRelay)
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
@@ -87,18 +87,14 @@
 
     def on_blocktxn(self, message): self.bad_message(message)
 
+
 # Node that never sends a version. We'll use this to send a bunch of messages
 # anyway, and eventually get disconnected.
 
 
 class CNodeNoVersionMisbehavior(CLazyNode):
-    # Send enough veracks without a message to reach the peer discouragement
-    # threshold. This should get us disconnected. NOTE: implementation-specific
-    # test; update if our discouragement policy for peer misbehavior changes.
-    def on_open(self):
-        super().on_open()
-        for _ in range(DISCOURAGEMENT_THRESHOLD):
-            self.send_message(msg_verack())
+    pass
+
 
 # Node that never sends a version. This one just sits idle and hopes to receive
 # any message (it shouldn't!)
@@ -108,6 +104,7 @@
     def __init__(self):
         super().__init__()
 
+
 # Node that sends a version but not a verack.
 
 
@@ -147,6 +144,11 @@
         no_verack_idlenode = self.nodes[0].add_p2p_connection(
             CNodeNoVerackIdle(), wait_for_verack=False)
 
+        # Send enough veracks without a message to reach the peer discouragement
+        # threshold. This should get us disconnected.
+        for _ in range(DISCOURAGEMENT_THRESHOLD):
+            no_version_disconnect_node.send_message(msg_verack())
+
         # 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()
@@ -194,7 +196,6 @@
             P2PInterface(), send_version=False, wait_for_verack=False)
         old_version_msg = msg_version()
         old_version_msg.nVersion = 31799
-        wait_until(lambda: p2p_old_node.is_connected)
         with self.nodes[0].assert_debug_log(['peer=4 using obsolete version 31799; disconnecting']):
             p2p_old_node.send_message(old_version_msg)
             p2p_old_node.wait_for_disconnect()
diff --git a/test/functional/test_framework/p2p.py b/test/functional/test_framework/p2p.py
--- a/test/functional/test_framework/p2p.py
+++ b/test/functional/test_framework/p2p.py
@@ -564,7 +564,7 @@
         def test_function():
             return "verack" in self.last_message
 
-        self.wait_until(test_function, timeout=timeout, check_connected=False)
+        self.wait_until(test_function, timeout=timeout)
 
     # Message sending helper functions
 
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
@@ -679,6 +679,9 @@
             net=self.chain,
             timeout_factor=self.timeout_factor)()
         self.p2ps.append(p2p_conn)
+        p2p_conn.wait_until(
+            lambda: p2p_conn.is_connected,
+            check_connected=False)
         if wait_for_verack:
             # Wait for the node to send us the version and verack
             p2p_conn.wait_for_verack()