diff --git a/graalpython/com.oracle.graal.python.test/src/tests/test_ssl.py b/graalpython/com.oracle.graal.python.test/src/tests/test_ssl.py
index f39f880ed5..daf4fa5fbb 100644
--- a/graalpython/com.oracle.graal.python.test/src/tests/test_ssl.py
+++ b/graalpython/com.oracle.graal.python.test/src/tests/test_ssl.py
@@ -405,6 +405,30 @@ def test_alpn(self):
         server, client = check_handshake(server_context, client_context)
         self.assertEqual(client.selected_alpn_protocol(), "http/1.1")
 
+
+class ProtocolSelectionTests(unittest.TestCase):
+
+    def check_protocol_availability_controls_selection(self, has_name, protocol_name, protocol_id):
+        if getattr(ssl, has_name):
+            self.assertTrue(hasattr(ssl, protocol_name))
+            ssl.SSLContext(getattr(ssl, protocol_name))
+        else:
+            protocol = getattr(ssl, protocol_name, protocol_id)
+            with self.assertRaisesRegex(ValueError, "invalid or unsupported protocol version"):
+                ssl.SSLContext(protocol)
+
+    def test_single_version_availability_controls_selection(self):
+        self.check_protocol_availability_controls_selection("HAS_SSLv3", "PROTOCOL_SSLv3", 1)
+        self.check_protocol_availability_controls_selection("HAS_TLSv1", "PROTOCOL_TLSv1", 3)
+        self.check_protocol_availability_controls_selection("HAS_TLSv1_1", "PROTOCOL_TLSv1_1", 4)
+        self.check_protocol_availability_controls_selection("HAS_TLSv1_2", "PROTOCOL_TLSv1_2", 5)
+
+    def test_generic_protocols_keep_sslv3_disabled(self):
+        for protocol in (ssl.PROTOCOL_TLS, ssl.PROTOCOL_TLS_CLIENT, ssl.PROTOCOL_TLS_SERVER):
+            with self.subTest(protocol=protocol):
+                self.assertTrue(ssl.SSLContext(protocol).options & ssl.OP_NO_SSLv3)
+
+
 def get_cipher_list(cipher_string):
     context = ssl.SSLContext()
     context.set_ciphers(cipher_string)
diff --git a/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/builtins/objects/ssl/SSLContextBuiltins.java b/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/builtins/objects/ssl/SSLContextBuiltins.java
index d1f6df16fc..2746186462 100644
--- a/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/builtins/objects/ssl/SSLContextBuiltins.java
+++ b/graalpython/com.oracle.graal.python/src/com/oracle/graal/python/builtins/objects/ssl/SSLContextBuiltins.java
@@ -173,7 +173,7 @@ static PSSLContext createContext(VirtualFrame frame, Object type, int protocol,
                         @Cached PConstructAndRaiseNode.Lazy constructAndRaiseNode,
                         @Cached PRaiseNode raiseNode) {
             SSLMethod method = SSLMethod.fromPythonId(protocol);
-            if (method == null) {
+            if (method == null || isUnsupportedSingleVersion(method)) {
                 throw raiseNode.raise(inliningTarget, ValueError, ErrorMessages.INVALID_OR_UNSUPPORTED_PROTOCOL_VERSION, "NULL");
             }
             try {
@@ -190,6 +190,9 @@ static PSSLContext createContext(VirtualFrame frame, Object type, int protocol,
                                 createSSLContext());
                 long options = SSLOptions.SSL_OP_ALL;
                 if (method != SSLMethod.SSL3) {
+                    // supportedProtocols describes runtime availability. This per-context option still keeps
+                    // generic TLS contexts from negotiating SSLv3. Only an explicit, supported SSLv3
+                    // context may leave it enabled.
                     options |= SSLOptions.SSL_OP_NO_SSLv3;
                 }
                 context.setOptions(options);
@@ -201,6 +204,19 @@ static PSSLContext createContext(VirtualFrame frame, Object type, int protocol,
             }
         }
 
+        @TruffleBoundary
+        private static boolean isUnsupportedSingleVersion(SSLMethod method) {
+            if (!method.isSingleVersion()) {
+                return false;
+            }
+            for (SSLProtocol supportedProtocol : SSLModuleBuiltins.getSupportedProtocols()) {
+                if (method.allowsProtocol(supportedProtocol)) {
+                    return false;
+                }
+            }
+            return true;
+        }
+
         @TruffleBoundary
         private static SSLContext createSSLContext() throws NoSuchAlgorithmException, KeyManagementException {
             SSLContext context = SSLContext.getInstance("TLS");