diff --git a/distributed/tests/test_asyncprocess.py b/distributed/tests/test_asyncprocess.py
index 44ba89bcc3e..65aa0e303cc 100644
--- a/distributed/tests/test_asyncprocess.py
+++ b/distributed/tests/test_asyncprocess.py
@@ -16,7 +16,7 @@
 from tornado.ioloop import IOLoop
 from tornado.locks import Event
 
-from distributed.compatibility import WINDOWS
+from distributed.compatibility import LINUX, MACOS, WINDOWS
 from distributed.metrics import time
 from distributed.process import AsyncProcess
 from distributed.utils import get_mp_context
@@ -36,10 +36,10 @@ def exit_now(rc=0):
     sys.exit(rc)
 
 
-def exit_with_signal(signum):
+def exit_with_sigint():
     signal.signal(signal.SIGINT, signal.SIG_DFL)
+    os.kill(os.getpid(), signal.SIGINT)
     while True:
-        os.kill(os.getpid(), signum)
         sleep(0.01)
 
 
@@ -159,45 +159,57 @@ async def test_exitcode():
     assert proc.exitcode is None
 
     q.put(5)
-    await proc.join(timeout=30)
+    await proc.join()
     assert not proc.is_alive()
     assert proc.exitcode == 5
 
 
-@pytest.mark.skipif(WINDOWS, reason="POSIX only")
+def assert_exit_code(proc: AsyncProcess, expect: signal.Signals) -> None:
+    if WINDOWS:
+        # multiprocessing.Process.terminate() sets exit code -15 like in Linux, but
+        # os.kill(pid, signal.SIGTERM) sets exit code +15
+        assert proc.exitcode in (-expect, expect)
+    elif MACOS:
+        # FIXME this happens very frequently on GitHub MacOSX CI. Reason unknown.
+        if expect != signal.SIGKILL and proc.exitcode == -signal.SIGKILL:
+            raise pytest.xfail(reason="https://github.com/dask/distributed/issues/6393")
+        assert proc.exitcode == -expect
+    else:
+        assert LINUX
+        assert proc.exitcode == -expect
+
+
 @gen_test()
-async def test_signal():
-    proc = AsyncProcess(target=exit_with_signal, args=(signal.SIGINT,))
-    proc.daemon = True
+async def test_sigint_from_same_process():
+    proc = AsyncProcess(target=exit_with_sigint)
     assert not proc.is_alive()
     assert proc.exitcode is None
 
     await proc.start()
-    await proc.join(timeout=30)
+    await proc.join()
 
     assert not proc.is_alive()
-    # Can be 255 with forkserver, see https://bugs.python.org/issue30589
-    assert proc.exitcode in (-signal.SIGINT, 255)
+    assert_exit_code(proc, signal.SIGINT)
 
+
+@gen_test()
+async def test_sigterm_from_parent_process():
     proc = AsyncProcess(target=wait)
     await proc.start()
     os.kill(proc.pid, signal.SIGTERM)
-    await proc.join(timeout=30)
-
+    await proc.join()
     assert not proc.is_alive()
-    assert proc.exitcode in (-signal.SIGTERM, 255)
+    assert_exit_code(proc, signal.SIGTERM)
 
 
 @gen_test()
 async def test_terminate():
     proc = AsyncProcess(target=wait)
-    proc.daemon = True
     await proc.start()
     await proc.terminate()
-
     await proc.join()
     assert not proc.is_alive()
-    assert proc.exitcode in (-signal.SIGTERM, 255)
+    assert_exit_code(proc, signal.SIGTERM)
 
 
 @gen_test()
@@ -333,7 +345,7 @@ async def test_kill():
     await proc.kill()
     await proc.join()
     assert not proc.is_alive()
-    assert proc.exitcode in (-signal.SIGKILL, 255)
+    assert proc.exitcode == -signal.SIGKILL
 
 
 def _worker_process(worker_ready, child_pipe):
diff --git a/distributed/tests/test_semaphore.py b/distributed/tests/test_semaphore.py
index c922c568dd5..2c4388af628 100644
--- a/distributed/tests/test_semaphore.py
+++ b/distributed/tests/test_semaphore.py
@@ -3,6 +3,7 @@
 import asyncio
 import logging
 import pickle
+import signal
 from datetime import timedelta
 from time import sleep
 
@@ -146,7 +147,7 @@ def f(x, sem, kill_address):
                     if worker.address == kill_address:
                         import os
 
-                        os.kill(os.getpid(), 15)
+                        os.kill(os.getpid(), signal.SIGTERM)
                     return x
 
             futures = client.map(