diff --git a/cheroot/errors.py b/cheroot/errors.py
index 4395e56528..91fac316ba 100644
--- a/cheroot/errors.py
+++ b/cheroot/errors.py
@@ -56,3 +56,24 @@ 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
+    broken_connection_exceptions = (BrokenPipeError, ConnectionResetError)
+except NameError:  # py2
+    broken_connection_exceptions = ()
diff --git a/cheroot/server.py b/cheroot/server.py
index a5c31b2e65..8ecf9265a2 100644
--- a/cheroot/server.py
+++ b/cheroot/server.py
@@ -75,7 +75,6 @@
 import platform
 import contextlib
 import threading
-import errno
 
 try:
     from functools import lru_cache
@@ -1478,9 +1477,10 @@ def _close_kernel_socket(self):
 
         try:
             shutdown(socket.SHUT_RDWR)  # actually send a TCP FIN
+        except errors.broken_connection_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