diff --git a/trio/_network.py b/trio/_network.py
index 6df9c666c7..ee5f80c0df 100644
--- a/trio/_network.py
+++ b/trio/_network.py
@@ -56,7 +56,7 @@ class SocketStream(HalfCloseableStream):
     def __init__(self, sock):
         if not tsocket.is_trio_socket(sock):
             raise TypeError("SocketStream requires trio socket object")
-        if sock._real_type != tsocket.SOCK_STREAM:
+        if tsocket._real_type(sock.type) != tsocket.SOCK_STREAM:
             raise ValueError("SocketStream requires a SOCK_STREAM socket")
         try:
             sock.getpeername()
diff --git a/trio/socket.py b/trio/socket.py
index 412e52f2fd..58e7f0a889 100644
--- a/trio/socket.py
+++ b/trio/socket.py
@@ -229,6 +229,13 @@ def is_trio_socket(obj):
     getattr(_stdlib_socket, "SOCK_NONBLOCK", 0)
     | getattr(_stdlib_socket, "SOCK_CLOEXEC", 0))
 
+# Hopefully Python will eventually make something like this public
+# (see bpo-21327) but I don't want to make it public myself and then
+# find out they picked a different name... this is used internally in
+# this file and also elsewhere in trio.
+def _real_type(type_num):
+    return type_num & _SOCK_TYPE_MASK
+
 class _SocketType:
     def __init__(self, sock):
         if type(sock) is not _stdlib_socket.socket:
@@ -241,12 +248,6 @@ def __init__(self, sock):
         self._sock.setblocking(False)
         self._did_SHUT_WR = False
 
-        # Hopefully Python will eventually make something like this public
-        # (see bpo-21327) but I don't want to make it public myself and then
-        # find out they picked a different name... this is used internally in
-        # this file and also elsewhere in trio.
-        self._real_type = sock.type & _SOCK_TYPE_MASK
-
         # Defaults:
         if self._sock.family == AF_INET6:
             try:
@@ -362,7 +363,7 @@ def _check_address(self, address, *, require_resolved):
                 _stdlib_socket.getaddrinfo(
                     address[0], address[1],
                     self._sock.family,
-                    self._real_type,
+                    _real_type(self._sock.type),
                     self._sock.proto,
                     flags=_NUMERIC_ONLY)
             except gaierror as exc:
@@ -399,7 +400,7 @@ async def _resolve_address(self, address, flags):
         gai_res = await getaddrinfo(
             address[0], address[1],
             self._sock.family,
-            self._real_type,
+            _real_type(self._sock.type),
             self._sock.proto,
             flags)
         # AFAICT from the spec it's not possible for getaddrinfo to return an