diff --git a/tests/test_ssl.py b/tests/test_ssl.py
index 63bfd117..ef274dd5 100644
--- a/tests/test_ssl.py
+++ b/tests/test_ssl.py
@@ -2,17 +2,31 @@ import os
 
 import pytest
 import pytest_httpbin.certs
-from requests.exceptions import SSLError
+import requests.exceptions
 
 from httpie import ExitStatus
 from httpie.input import SSL_VERSION_ARG_MAPPING
-from utils import http, HTTP_OK, TESTS_ROOT
+from utils import HTTP_OK, TESTS_ROOT, http
+
+
+try:
+    # Handle OpenSSL errors, if installed.
+    # See <https://github.com/jakubroztocil/httpie/issues/729>
+    # noinspection PyUnresolvedReferences
+    import OpenSSL.SSL
+    ssl_errors = (
+        requests.exceptions.SSLError,
+        OpenSSL.SSL.Error,
+    )
+except ImportError:
+    ssl_errors = (
+        requests.exceptions.SSLError,
+    )
 
 
 CLIENT_CERT = os.path.join(TESTS_ROOT, 'client_certs', 'client.crt')
 CLIENT_KEY = os.path.join(TESTS_ROOT, 'client_certs', 'client.key')
 CLIENT_PEM = os.path.join(TESTS_ROOT, 'client_certs', 'client.pem')
-
 # FIXME:
 # We test against a local httpbin instance which uses a self-signed cert.
 # Requests without --verify=<CA_BUNDLE> will fail with a verification error.
@@ -28,7 +42,7 @@ def test_ssl_version(httpbin_secure, ssl_version):
             httpbin_secure + '/get'
         )
         assert HTTP_OK in r
-    except SSLError as e:
+    except ssl_errors as e:
         if ssl_version == 'ssl3':
             # pytest-httpbin doesn't support ssl3
             assert 'SSLV3_ALERT_HANDSHAKE_FAILURE' in str(e)
@@ -57,12 +71,12 @@ class TestClientCert:
         assert 'No such file or directory' in r.stderr
 
     def test_cert_file_invalid(self, httpbin_secure):
-        with pytest.raises(SSLError):
+        with pytest.raises(ssl_errors):
             http(httpbin_secure + '/get',
                  '--cert', __file__)
 
     def test_cert_ok_but_missing_key(self, httpbin_secure):
-        with pytest.raises(SSLError):
+        with pytest.raises(ssl_errors):
             http(httpbin_secure + '/get',
                  '--cert', CLIENT_CERT)
 
@@ -79,21 +93,23 @@ class TestServerCert:
         assert HTTP_OK in r
 
     def test_verify_custom_ca_bundle_path(
-            self, httpbin_secure_untrusted):
+        self, httpbin_secure_untrusted
+    ):
         r = http(httpbin_secure_untrusted + '/get', '--verify', CA_BUNDLE)
         assert HTTP_OK in r
 
     def test_self_signed_server_cert_by_default_raises_ssl_error(
-            self,
-            httpbin_secure_untrusted):
-        with pytest.raises(SSLError):
+        self,
+        httpbin_secure_untrusted
+    ):
+        with pytest.raises(ssl_errors):
             http(httpbin_secure_untrusted.url + '/get')
 
     def test_verify_custom_ca_bundle_invalid_path(self, httpbin_secure):
         # since 2.14.0 requests raises IOError
-        with pytest.raises((SSLError, IOError)):
+        with pytest.raises(ssl_errors + (IOError,)):
             http(httpbin_secure.url + '/get', '--verify', '/__not_found__')
 
     def test_verify_custom_ca_bundle_invalid_bundle(self, httpbin_secure):
-        with pytest.raises(SSLError):
+        with pytest.raises(ssl_errors):
             http(httpbin_secure.url + '/get', '--verify', __file__)