diff --git a/Lib/socketserver.py b/Lib/socketserver.py
index 6859b69682e..57c1ae6e9e8 100644
--- a/Lib/socketserver.py
+++ b/Lib/socketserver.py
@@ -128,7 +128,6 @@ import selectors
 import os
 import sys
 import threading
-import contextlib
 from io import BufferedIOBase
 from time import monotonic as time
 
@@ -629,55 +628,6 @@ if hasattr(os, "fork"):
             self.collect_children(blocking=self.block_on_close)
 
 
-class _Threads(list):
-    """
-    Joinable list of all non-daemon threads.
-    """
-    def __init__(self):
-        self._lock = threading.Lock()
-
-    def append(self, thread):
-        if thread.daemon:
-            return
-        with self._lock:
-            super().append(thread)
-
-    def remove(self, thread):
-        with self._lock:
-            # should not happen, but safe to ignore
-            with contextlib.suppress(ValueError):
-                super().remove(thread)
-
-    def remove_current(self):
-        """Remove a current non-daemon thread."""
-        thread = threading.current_thread()
-        if not thread.daemon:
-            self.remove(thread)
-
-    def pop_all(self):
-        with self._lock:
-            self[:], result = [], self[:]
-        return result
-
-    def join(self):
-        for thread in self.pop_all():
-            thread.join()
-
-
-class _NoThreads:
-    """
-    Degenerate version of _Threads.
-    """
-    def append(self, thread):
-        pass
-
-    def join(self):
-        pass
-
-    def remove_current(self):
-        pass
-
-
 class ThreadingMixIn:
     """Mix-in class to handle each request in a new thread."""
 
@@ -686,9 +636,9 @@ class ThreadingMixIn:
     daemon_threads = False
     # If true, server_close() waits until all non-daemonic threads terminate.
     block_on_close = True
-    # Threads object
+    # For non-daemonic threads, list of threading.Threading objects
     # used by server_close() to wait for all threads completion.
-    _threads = _NoThreads()
+    _threads = None
 
     def process_request_thread(self, request, client_address):
         """Same as in BaseServer but as a thread.
@@ -701,24 +651,27 @@ class ThreadingMixIn:
         except Exception:
             self.handle_error(request, client_address)
         finally:
-            try:
-                self.shutdown_request(request)
-            finally:
-                self._threads.remove_current()
+            self.shutdown_request(request)
 
     def process_request(self, request, client_address):
         """Start a new thread to process the request."""
-        if self.block_on_close:
-            vars(self).setdefault('_threads', _Threads())
         t = threading.Thread(target = self.process_request_thread,
                              args = (request, client_address))
         t.daemon = self.daemon_threads
-        self._threads.append(t)
+        if not t.daemon and self.block_on_close:
+            if self._threads is None:
+                self._threads = []
+            self._threads.append(t)
         t.start()
 
     def server_close(self):
         super().server_close()
-        self._threads.join()
+        if self.block_on_close:
+            threads = self._threads
+            self._threads = None
+            if threads:
+                for thread in threads:
+                    thread.join()
 
 
 if hasattr(os, "fork"):
diff --git a/Lib/test/test_socketserver.py b/Lib/test/test_socketserver.py
index 1944795f058..7cdd115a951 100644
--- a/Lib/test/test_socketserver.py
+++ b/Lib/test/test_socketserver.py
@@ -277,13 +277,6 @@ class SocketServerTest(unittest.TestCase):
             t.join()
             s.server_close()
 
-    def test_close_immediately(self):
-        class MyServer(socketserver.ThreadingMixIn, socketserver.TCPServer):
-            pass
-
-        server = MyServer((HOST, 0), lambda: None)
-        server.server_close()
-
     def test_tcpserver_bind_leak(self):
         # Issue #22435: the server socket wouldn't be closed if bind()/listen()
         # failed.
@@ -498,23 +491,6 @@ class MiscTestCase(unittest.TestCase):
         self.assertEqual(server.shutdown_called, 1)
         server.server_close()
 
-    def test_threads_reaped(self):
-        """
-        In #37193, users reported a memory leak
-        due to the saving of every request thread. Ensure that the
-        threads are cleaned up after the requests complete.
-        """
-        class MyServer(socketserver.ThreadingMixIn, socketserver.TCPServer):
-            pass
-
-        server = MyServer((HOST, 0), socketserver.StreamRequestHandler)
-        for n in range(10):
-            with socket.create_connection(server.server_address):
-                server.handle_request()
-        [thread.join() for thread in server._threads]
-        self.assertEqual(len(server._threads), 0)
-        server.server_close()
-
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/Misc/NEWS.d/next/Library/2020-06-12-21-23-20.bpo-37193.wJximU.rst b/Misc/NEWS.d/next/Library/2020-06-12-21-23-20.bpo-37193.wJximU.rst
deleted file mode 100644
index fbf56d3194c..00000000000
--- a/Misc/NEWS.d/next/Library/2020-06-12-21-23-20.bpo-37193.wJximU.rst
+++ /dev/null
@@ -1,2 +0,0 @@
-Fixed memory leak in ``socketserver.ThreadingMixIn`` introduced in Python
-3.7.