diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 14d3cc1e96c..34e86767562 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -670,9 +670,7 @@ class ContextTests(unittest.TestCase):
     @skip_if_broken_ubuntu_ssl
     def test_options(self):
         ctx = ssl.SSLContext(ssl.PROTOCOL_TLSv1)
-        # OP_ALL is the default value
-        self.assertEqual(ssl.OP_ALL, ctx.options)
-        ctx.options |= ssl.OP_NO_SSLv2
+        # OP_ALL | OP_NO_SSLv2 is the default value
         self.assertEqual(ssl.OP_ALL | ssl.OP_NO_SSLv2,
                          ctx.options)
         ctx.options |= ssl.OP_NO_SSLv3
@@ -2095,7 +2093,7 @@ else:
             try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv2, True)
             try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv2, True, ssl.CERT_OPTIONAL)
             try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv2, True, ssl.CERT_REQUIRED)
-            try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv23, True)
+            try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv23, False)
             try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv3, False)
             try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_TLSv1, False)
             # SSLv23 client with specific SSL options
@@ -2103,9 +2101,9 @@ else:
                 # No SSLv2 => client will use an SSLv3 hello on recent OpenSSLs
                 try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv23, False,
                                    client_options=ssl.OP_NO_SSLv2)
-            try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv23, True,
+            try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv23, False,
                                client_options=ssl.OP_NO_SSLv3)
-            try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv23, True,
+            try_protocol_combo(ssl.PROTOCOL_SSLv2, ssl.PROTOCOL_SSLv23, False,
                                client_options=ssl.OP_NO_TLSv1)
 
         @skip_if_broken_ubuntu_ssl
diff --git a/Misc/NEWS b/Misc/NEWS
index cb59a68a1e8..e58df2a3357 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -25,6 +25,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #20207: Always disable SSLv2 except when PROTOCOL_SSLv2 is explicitly
+  asked for.
+
 - Issue #18960: The tokenize module now ignore the source encoding declaration
   on the second line if the first line contains anything except a comment.
 
diff --git a/Modules/_ssl.c b/Modules/_ssl.c
index a370b1b41e2..2e3c5b1187e 100644
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -134,9 +134,7 @@ enum py_ssl_cert_requirements {
 };
 
 enum py_ssl_version {
-#ifndef OPENSSL_NO_SSL2
     PY_SSL_VERSION_SSL2,
-#endif
     PY_SSL_VERSION_SSL3=1,
     PY_SSL_VERSION_SSL23,
 #if HAVE_TLSv1_2
@@ -1999,6 +1997,7 @@ context_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
     char *kwlist[] = {"protocol", NULL};
     PySSLContext *self;
     int proto_version = PY_SSL_VERSION_SSL23;
+    long options;
     SSL_CTX *ctx = NULL;
 
     if (!PyArg_ParseTupleAndKeywords(
@@ -2055,8 +2054,10 @@ context_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
     self->check_hostname = 0;
     /* Defaults */
     SSL_CTX_set_verify(self->ctx, SSL_VERIFY_NONE, NULL);
-    SSL_CTX_set_options(self->ctx,
-                        SSL_OP_ALL & ~SSL_OP_DONT_INSERT_EMPTY_FRAGMENTS);
+    options = SSL_OP_ALL & ~SSL_OP_DONT_INSERT_EMPTY_FRAGMENTS;
+    if (proto_version != PY_SSL_VERSION_SSL2)
+        options |= SSL_OP_NO_SSLv2;
+    SSL_CTX_set_options(self->ctx, options);
 
 #define SID_CTX "Python"
     SSL_CTX_set_session_id_context(self->ctx, (const unsigned char *) SID_CTX,