diff --git a/cheroot/test/test_ssl.py b/cheroot/test/test_ssl.py
index fe8a0a0..92a77c1 100644
--- a/cheroot/test/test_ssl.py
+++ b/cheroot/test/test_ssl.py
@@ -316,11 +316,9 @@ def test_tls_client_auth(
         expected_ssl_errors = (
             requests.exceptions.SSLError,
             OpenSSL.SSL.Error,
-        ) if PY34 else (
-            requests.exceptions.SSLError,
+            requests.exceptions.ConnectionError,
         )
-        if IS_WINDOWS:
-            expected_ssl_errors += requests.exceptions.ConnectionError,
+
         with pytest.raises(expected_ssl_errors) as ssl_err:
             make_https_request()
 
@@ -335,7 +333,7 @@ def test_tls_client_auth(
         except AttributeError:
             if PY34:
                 pytest.xfail('OpenSSL behaves wierdly under Python 3.4')
-            elif six.PY3 and IS_WINDOWS:
+            elif six.PY3:
                 err_text = str(ssl_err.value)
             else:
                 raise
@@ -348,8 +346,7 @@ def test_tls_client_auth(
             if IS_MACOS and IS_PYPY and adapter_type == 'pyopenssl':
                 expected_substrings = ('tlsv1 alert unknown ca', )
             if (
-                    IS_WINDOWS
-                    and tls_verify_mode in (
+                    tls_verify_mode in (
                         ssl.CERT_REQUIRED,
                         ssl.CERT_OPTIONAL,
                     )
@@ -361,6 +358,7 @@ def test_tls_client_auth(
                     "SysCallError(10054, 'WSAECONNRESET')",
                     "('Connection aborted.', "
                     'OSError("(10054, \'WSAECONNRESET\')"))',
+                    'OSError("(104, \'ECONNRESET\')"))',
                 )
         assert any(e in err_text for e in expected_substrings)