pytest: move benchmark in test_connection.py to tests/benchmarks.py

diff --git a/tests/benchmark.py b/tests/benchmark.py
index ec0062e8..97d26f60 100644
--- a/tests/benchmark.py
+++ b/tests/benchmark.py
@@ -1,7 +1,8 @@
 from concurrent import futures
 from fixtures import *  # noqa: F401,F403
+from pyln.client import RpcError
 from tqdm import tqdm
-from utils import (wait_for, TIMEOUT)
+from utils import (wait_for, TIMEOUT, only_one)
 
 
 import os
@@ -228,3 +229,36 @@ def test_spam_listcommands(node_factory, bitcoind, benchmark):
 
     # This calls "listinvoice" 100,000 times (which doesn't need a transaction commit)
     benchmark(l1.rpc.spamlistcommand, 100_000)
+
+
+def test_payment_speed(node_factory, benchmark):
+    """This makes sure we don't screw up nagle handling.
+
+    Normally:
+    Name (time in ms)           Min       Max      Mean  StdDev    Median     IQR  Outliers     OPS  Rounds  Iterations
+    test_payment_speed      16.3587  40.4925  27.4874  5.5512  27.7885  8.9291       9;0  36.3803      33           1
+
+    Without TCP_NODELAY:
+    Name (time in ms)           Min       Max      Mean  StdDev    Median     IQR  Outliers     OPS  Rounds  Iterations
+    test_payment_speed     153.7132  163.2027  158.6747  3.4059  158.5219  6.3745       3;0  6.3022       9           1
+    """
+    l1 = get_bench_node(node_factory, extra_options={'commit-time': 0})
+    l2 = get_bench_node(node_factory, extra_options={'commit-time': 0})
+
+    node_factory.join_nodes([l1, l2])
+
+    scid = only_one(l1.rpc.listpeerchannels()['channels'])['short_channel_id']
+    routestep = {
+        'amount_msat': 100,
+        'id': l2.info['id'],
+        'delay': 5,
+        'channel': scid
+    }
+
+    def onepay(l1, routestep):
+        phash = random.randbytes(32).hex()
+        l1.rpc.sendpay([routestep], phash)
+        with pytest.raises(RpcError, match="WIRE_INCORRECT_OR_UNKNOWN_PAYMENT_DETAILS"):
+            l1.rpc.waitsendpay(phash)
+
+    benchmark(onepay, l1, routestep)
diff --git a/tests/test_connection.py b/tests/test_connection.py
index bd887416..37530022 100644
--- a/tests/test_connection.py
+++ b/tests/test_connection.py
@@ -4579,41 +4579,6 @@ def test_no_delay(node_factory):
     assert end < start + 100 * 0.5
 
 
-@unittest.skipIf(os.getenv('TEST_BENCH', '0') == '0', "For profiling")
-def test_bench(node_factory):
-    """Is our Nagle disabling for critical messages working?"""
-    l1, l2 = node_factory.get_nodes(2, opts={'start': False,
-                                             'commit-time': 0})
-
-    # memleak detection plays havoc with profiles.
-    del l1.daemon.env["LIGHTNINGD_DEV_MEMLEAK"]
-    del l2.daemon.env["LIGHTNINGD_DEV_MEMLEAK"]
-
-    l1.start()
-    l2.start()
-    node_factory.join_nodes([l1, l2])
-
-    scid = only_one(l1.rpc.listpeerchannels()['channels'])['short_channel_id']
-    routestep = {
-        'amount_msat': 100,
-        'id': l2.info['id'],
-        'delay': 5,
-        'channel': scid
-    }
-
-    start = time.time()
-    # If we were stupid enough to leave Nagle enabled, this would add 200ms
-    # seconds delays each way!
-    for _ in range(1000):
-        phash = random.randbytes(32).hex()
-        l1.rpc.sendpay([routestep], phash)
-        with pytest.raises(RpcError, match="WIRE_INCORRECT_OR_UNKNOWN_PAYMENT_DETAILS"):
-            l1.rpc.waitsendpay(phash)
-    end = time.time()
-    duration = end - start
-    assert duration == 0
-
-
 def test_listpeerchannels_by_scid(node_factory):
     l1, l2, l3 = node_factory.line_graph(3, announce_channels=False)