diff --git a/cheroot/ssl/builtin.py b/cheroot/ssl/builtin.py
index 2501f2e3db..871d1d545b 100644
--- a/cheroot/ssl/builtin.py
+++ b/cheroot/ssl/builtin.py
@@ -272,20 +272,21 @@ def bind(self, sock):
 
     def wrap(self, sock):
         """Wrap and return the given socket, plus WSGI environ entries."""
+        EMPTY_RESULT = None, {}
         try:
             s = self.context.wrap_socket(
                 sock, do_handshake_on_connect=True, server_side=True,
             )
-            return s, self.get_environ(s)
         except ssl.SSLError as ex:
             if ex.errno == ssl.SSL_ERROR_SSL:
                 if _assert_ssl_exc_contains(ex, 'http request'):
                     # The client is speaking HTTP to an HTTPS server.
                     raise errors.NoSSLError
-        except (generic_socket_error, ssl.SSLZeroReturnError):
+        except generic_socket_error:
             pass
-        # empty result
-        return None, {}
+        else:
+            return s, self.get_environ(s)
+        return EMPTY_RESULT
 
     def get_environ(self, sock):
         """Create WSGI environ entries to be merged into each request."""