diff --git a/Lib/ssl.py b/Lib/ssl.py
index 8ad4a33..27842b3 100644
--- a/Lib/ssl.py
+++ b/Lib/ssl.py
@@ -749,9 +749,9 @@ class SSLSocket(socket):
             self.ssl_version = ssl_version
             self.ca_certs = ca_certs
             self.ciphers = ciphers
-        # Can't use sock.type as other flags (such as SOCK_NONBLOCK) get
-        # mixed in.
-        if sock.getsockopt(SOL_SOCKET, SO_TYPE) != SOCK_STREAM:
+        if sock is not None:
+            type = sock.type
+        if type & SOCK_STREAM != SOCK_STREAM:
             raise NotImplementedError("only stream sockets are supported")
         if server_side:
             if server_hostname:
diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index d203cdd..c80c782 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -181,6 +181,26 @@ class BasicSocketTests(unittest.TestCase):
         ctx = ssl.SSLContext(proto)
         self.assertIs(ctx.protocol, proto)

+    def test_constructor(self):
+        s = socket.socket()
+        sfd = s.fileno()
+
+        # Create secure socket from socket
+        ss = ssl.SSLSocket(sock=s)
+        self.assertTrue(ss.fileno() == sfd)
+
+        s = socket.socket()
+        sfd = s.detach()
+
+        # Create secure socket from scratch
+        ss = ssl.SSLSocket()
+        self.assertTrue(ss.fileno() >= 0)
+        self.assertTrue(ss.fileno() != sfd)
+
+        # Create secure socket from fileno
+        ss = ssl.SSLSocket(fileno=sfd)
+        self.assertTrue(ss.fileno() == sfd)
+
     def test_random(self):
         v = ssl.RAND_status()
         if support.verbose: