diff --git a/Doc/library/threading.rst b/Doc/library/threading.rst
index b94021b4eb8f89..e6185c5b3a214c 100644
--- a/Doc/library/threading.rst
+++ b/Doc/library/threading.rst
@@ -400,7 +400,8 @@ All methods are executed atomically.
          The *timeout* parameter is new.
 
       .. versionchanged:: 3.2
-         Lock acquires can now be interrupted by signals on POSIX.
+         Lock acquisition can now be interrupted by signals on POSIX if the
+         underlying threading implementation supports it.
 
 
    .. method:: release()
diff --git a/Lib/test/test_threadsignals.py b/Lib/test/test_threadsignals.py
index 1ad6c63fea2e35..7e13b1720f91e9 100644
--- a/Lib/test/test_threadsignals.py
+++ b/Lib/test/test_threadsignals.py
@@ -78,6 +78,10 @@ def alarm_interrupt(self, sig, frame):
 
     @unittest.skipIf(USING_PTHREAD_COND,
                      'POSIX condition variables cannot be interrupted')
+    @unittest.skipIf(sys.platform.startswith('linux') and
+                     not sys.thread_info.version,
+                     'Issue 34004: musl does not allow interruption of locks '
+                     'by signals.')
     # Issue #20564: sem_timedwait() cannot be interrupted on OpenBSD
     @unittest.skipIf(sys.platform.startswith('openbsd'),
                      'lock cannot be interrupted on OpenBSD')
@@ -105,6 +109,10 @@ def test_lock_acquire_interruption(self):
 
     @unittest.skipIf(USING_PTHREAD_COND,
                      'POSIX condition variables cannot be interrupted')
+    @unittest.skipIf(sys.platform.startswith('linux') and
+                     not sys.thread_info.version,
+                     'Issue 34004: musl does not allow interruption of locks '
+                     'by signals.')
     # Issue #20564: sem_timedwait() cannot be interrupted on OpenBSD
     @unittest.skipIf(sys.platform.startswith('openbsd'),
                      'lock cannot be interrupted on OpenBSD')