diff --git a/tests/test_connection.py b/tests/test_connection.py
index fd94b1e01eaa..4b2c6a2cd5b3 100644
--- a/tests/test_connection.py
+++ b/tests/test_connection.py
@@ -166,7 +166,6 @@ def test_bad_opening(node_factory):
 
 @unittest.skipIf(not DEVELOPER, "gossip without DEVELOPER=1 is slow")
 @unittest.skipIf(TEST_NETWORK != 'regtest', "Fee computation and limits are network specific")
-@pytest.mark.slow_test
 def test_opening_tiny_channel(node_factory):
     # Test custom min-capacity-sat parameters
     #
@@ -2586,16 +2585,10 @@ def test_fulfill_incoming_first(node_factory, bitcoind):
 
 
 @unittest.skipIf(not DEVELOPER, "gossip without DEVELOPER=1 is slow")
-@pytest.mark.slow_test
+@unittest.skipIf(VALGRIND, "Too memory hungry under valgrind")
 def test_restart_many_payments(node_factory, bitcoind):
     l1 = node_factory.get_node(may_reconnect=True)
-
-    # On my laptop, these take 89 seconds and 12 seconds
-    if node_factory.valgrind:
-        num = 2
-    else:
-        num = 5
-
+    num = 5
     nodes = node_factory.get_nodes(num * 2, opts={'may_reconnect': True})
     innodes = nodes[:num]
     outnodes = nodes[num:]
@@ -2883,13 +2876,11 @@ def test_feerate_stress(node_factory, executor):
 
 
 @unittest.skipIf(not DEVELOPER, "need dev_disconnect")
-@pytest.mark.slow_test
+@unittest.skipIf(VALGRIND, "Reconnection slow due to process spawning")
 def test_pay_disconnect_stress(node_factory, executor):
     """Expose race in htlc restoration in channeld: 50% chance of failure"""
-    if node_factory.valgrind:
-        NUM_RUNS = 2
-    else:
-        NUM_RUNS = 5
+    NUM_RUNS = 5
+
     for i in range(NUM_RUNS):
         l1, l2 = node_factory.line_graph(2, opts=[{'may_reconnect': True},
                                                   {'may_reconnect': True,