--- a/tests/test_rsa.py
+++ b/tests/test_rsa.py
@@ -113,6 +113,8 @@ class RSATestCase(unittest.TestCase):
         with self.assertRaises(TypeError):
             priv.private_encrypt(self.gen_callback, RSA.pkcs1_padding)
 
+    @unittest.skipIf(m2.OPENSSL_VERSION_NUMBER < 0x1010103f,
+                     'Relies on fix which happened only in OpenSSL 1.1.1c')
     def test_public_encrypt(self):
         priv = RSA.load_key(self.privkey)
         # pkcs1_padding, pkcs1_oaep_padding
@@ -124,13 +126,11 @@ class RSATestCase(unittest.TestCase):
 
         # sslv23_padding
         ctxt = priv.public_encrypt(self.data, RSA.sslv23_padding)
-        with self.assertRaises(RSA.RSAError):
-            priv.private_decrypt(ctxt, RSA.sslv23_padding)
-        with self.assertRaises(RSA.RSAError):
-            priv.private_decrypt(ctxt, RSA.sslv23_padding)
+        res = priv.private_decrypt(ctxt, RSA.sslv23_padding)
+        self.assertEqual(res, self.data)
 
         # no_padding
-        with self.assertRaises(RSA.RSAError):
+        with six.assertRaisesRegex(self, TypeError, 'data too small'):
             priv.public_encrypt(self.data, RSA.no_padding)
 
         # Type-check the data to be encrypted.