diff --git a/CHANGES.rst b/CHANGES.rst
index 134e3ff27f..189e79a7be 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -6,6 +6,9 @@
   waiting for a ``tick`` event, addressing performance
   degradation introduced in v8.1.0.
 
+- :issue:`341` via :pr:`342`: Suppress legitimate OS errors
+  expected on shutdown.
+
 .. scm-version-title:: v8.4.8
 
 - :issue:`317` via :pr:`337`: Fixed a regression in
diff --git a/cheroot/errors.py b/cheroot/errors.py
index 4395e56528..4101fe3e4a 100644
--- a/cheroot/errors.py
+++ b/cheroot/errors.py
@@ -1,3 +1,4 @@
+# -*- coding: utf-8 -*-
 """Collection of exceptions raised and/or processed by Cheroot."""
 
 from __future__ import absolute_import, division, print_function
@@ -56,3 +57,24 @@ def plat_specific_errors(*errnames):
 if sys.platform == 'darwin':
     socket_errors_to_ignore.extend(plat_specific_errors('EPROTOTYPE'))
     socket_errors_nonblocking.extend(plat_specific_errors('EPROTOTYPE'))
+
+
+acceptable_sock_shutdown_error_codes = {
+    errno.ENOTCONN,
+    errno.EPIPE, errno.ESHUTDOWN,  # corresponds to BrokenPipeError in Python 3
+    errno.ECONNRESET,  # corresponds to ConnectionResetError in Python 3
+}
+"""Errors that may happen during the connection close sequence.
+
+* ENOTCONN — client is no longer connected
+* EPIPE — write on a pipe while the other end has been closed
+* ESHUTDOWN — write on a socket which has been shutdown for writing
+* ECONNRESET — connection is reset by the peer
+
+Ref: https://github.com/cherrypy/cheroot/issues/341#issuecomment-735884889
+"""
+
+try:  # py3
+    acceptable_sock_shutdown_exceptions = (BrokenPipeError, ConnectionResetError)
+except NameError:  # py2
+    acceptable_sock_shutdown_exceptions = ()
diff --git a/cheroot/server.py b/cheroot/server.py
index fb3bc421a2..c75b2eba28 100644
--- a/cheroot/server.py
+++ b/cheroot/server.py
@@ -76,7 +76,6 @@
 import platform
 import contextlib
 import threading
-import errno
 
 try:
     from functools import lru_cache
@@ -1479,9 +1478,10 @@ def _close_kernel_socket(self):
 
         try:
             shutdown(socket.SHUT_RDWR)  # actually send a TCP FIN
+        except errors.acceptable_sock_shutdown_exceptions:
+            pass
         except socket.error as e:
-            # Suppress "client is no longer connected"
-            if e.errno != errno.ENOTCONN:
+            if e.errno not in errors.acceptable_sock_shutdown_error_codes:
                 raise