diff --git a/Lib/test/test_ftplib.py b/Lib/test/test_ftplib.py
index fa9c6f4..d3be7d6 100644
--- a/Lib/test/test_ftplib.py
+++ b/Lib/test/test_ftplib.py
@@ -889,7 +889,7 @@
 
     def test_auth_ssl(self):
         try:
-            self.client.ssl_version = ssl.PROTOCOL_SSLv3
+            self.client.ssl_version = ssl.PROTOCOL_SSLv23
             self.client.auth()
             self.assertRaises(ValueError, self.client.auth)
         finally:
diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 928f5e6..2dea0c5 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -2168,20 +2168,24 @@
                         sys.stdout.write(
                             " SSL2 client to SSL23 server test unexpectedly failed:\n %s\n"
                             % str(x))
-            try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, True)
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, True)
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv23, True)
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_TLSv1, True)
 
-            try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, True, ssl.CERT_OPTIONAL)
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, True, ssl.CERT_OPTIONAL)
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv23, True, ssl.CERT_OPTIONAL)
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_TLSv1, True, ssl.CERT_OPTIONAL)
 
-            try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, True, ssl.CERT_REQUIRED)
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, True, ssl.CERT_REQUIRED)
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv23, True, ssl.CERT_REQUIRED)
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_TLSv1, True, ssl.CERT_REQUIRED)
 
             # Server with specific SSL options
-            try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, False,
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv3, False,
                                server_options=ssl.OP_NO_SSLv3)
             # Will choose TLSv1
             try_protocol_combo(ssl.PROTOCOL_SSLv23, ssl.PROTOCOL_SSLv23, True,
@@ -2191,6 +2195,8 @@
 
 
         @skip_if_broken_ubuntu_ssl
+        @unittest.skipUnless(hasattr(ssl, 'PROTOCOL_SSLv3'),
+                             "OpenSSL is compiled without SSLv3 support")
         def test_protocol_sslv3(self):
             """Connecting to an SSLv3 server with various client options"""
             if support.verbose:
@@ -2218,7 +2224,8 @@
             try_protocol_combo(ssl.PROTOCOL_TLSv1, ssl.PROTOCOL_TLSv1, True, ssl.CERT_REQUIRED)
             if hasattr(ssl, 'PROTOCOL_SSLv2'):
                 try_protocol_combo(ssl.PROTOCOL_TLSv1, ssl.PROTOCOL_SSLv2, False)
-            try_protocol_combo(ssl.PROTOCOL_TLSv1, ssl.PROTOCOL_SSLv3, False)
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_TLSv1, ssl.PROTOCOL_SSLv3, False)
             try_protocol_combo(ssl.PROTOCOL_TLSv1, ssl.PROTOCOL_SSLv23, False,
                                client_options=ssl.OP_NO_TLSv1)
 
@@ -2233,7 +2240,8 @@
             try_protocol_combo(ssl.PROTOCOL_TLSv1_1, ssl.PROTOCOL_TLSv1_1, True)
             if hasattr(ssl, 'PROTOCOL_SSLv2'):
                 try_protocol_combo(ssl.PROTOCOL_TLSv1_1, ssl.PROTOCOL_SSLv2, False)
-            try_protocol_combo(ssl.PROTOCOL_TLSv1_1, ssl.PROTOCOL_SSLv3, False)
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_TLSv1_1, ssl.PROTOCOL_SSLv3, False)
             try_protocol_combo(ssl.PROTOCOL_TLSv1_1, ssl.PROTOCOL_SSLv23, False,
                                client_options=ssl.OP_NO_TLSv1_1)
 
@@ -2255,7 +2263,8 @@
                                client_options=ssl.OP_NO_SSLv3|ssl.OP_NO_SSLv2,)
             if hasattr(ssl, 'PROTOCOL_SSLv2'):
                 try_protocol_combo(ssl.PROTOCOL_TLSv1_2, ssl.PROTOCOL_SSLv2, False)
-            try_protocol_combo(ssl.PROTOCOL_TLSv1_2, ssl.PROTOCOL_SSLv3, False)
+            if hasattr(ssl, 'PROTOCOL_SSLv3'):
+                try_protocol_combo(ssl.PROTOCOL_TLSv1_2, ssl.PROTOCOL_SSLv3, False)
             try_protocol_combo(ssl.PROTOCOL_TLSv1_2, ssl.PROTOCOL_SSLv23, False,
                                client_options=ssl.OP_NO_TLSv1_2)
 
diff --git a/Misc/NEWS b/Misc/NEWS
index 7d6a99b..d5bb074 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -215,6 +215,9 @@
 Build
 -----
 
+- Issue #22935: Allow the ssl module to be compiled if openssl doesn't support
+  SSL 3.
+
 - Issue #16537: Check whether self.extensions is empty in setup.py. Patch by
   Jonathan Hosmer.
 
diff --git a/Modules/_ssl.c b/Modules/_ssl.c
index 90bca98..17beaf8 100644
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -2016,8 +2016,10 @@
     else if (proto_version == PY_SSL_VERSION_TLS1_2)
         ctx = SSL_CTX_new(TLSv1_2_method());
 #endif
+#ifndef OPENSSL_NO_SSL3
     else if (proto_version == PY_SSL_VERSION_SSL3)
         ctx = SSL_CTX_new(SSLv3_method());
+#endif
 #ifndef OPENSSL_NO_SSL2
     else if (proto_version == PY_SSL_VERSION_SSL2)
         ctx = SSL_CTX_new(SSLv2_method());
@@ -4065,8 +4067,10 @@
     PyModule_AddIntConstant(m, "PROTOCOL_SSLv2",
                             PY_SSL_VERSION_SSL2);
 #endif
+#ifndef OPENSSL_NO_SSL3
     PyModule_AddIntConstant(m, "PROTOCOL_SSLv3",
                             PY_SSL_VERSION_SSL3);
+#endif
     PyModule_AddIntConstant(m, "PROTOCOL_SSLv23",
                             PY_SSL_VERSION_SSL23);
     PyModule_AddIntConstant(m, "PROTOCOL_TLSv1",