diff --git a/Lib/test/test_socket.py b/Lib/test/test_socket.py
index 299e7212966ae3d..99f9e746c854e32 100644
--- a/Lib/test/test_socket.py
+++ b/Lib/test/test_socket.py
@@ -59,6 +59,9 @@
 # SCM_RIGHTS control message when several are sent in a single sendmsg().
 BSD_COMBINES_SCM_RIGHTS = sys.platform.startswith(
     ("netbsd", "openbsd", "dragonfly"))
+# OpenBSD and DragonFly fail recvmsg() with EMSGSIZE, instead of setting
+# MSG_CTRUNC, when the ancillary data buffer is too small for a cmsghdr.
+CMSG_TRUNC_RAISES_EMSGSIZE = sys.platform.startswith(("openbsd", "dragonfly"))
 WSL = "microsoft-standard-WSL" in platform.release()
 
 try:
@@ -4351,6 +4354,7 @@ def _testCmsgTrunc0(self):
     # (but still too small) buffer sizes.
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTrunc1(self):
         self.checkTruncatedHeader(self.doRecvmsg(self.serv_sock, len(MSG), 1))
 
@@ -4359,6 +4363,7 @@ def _testCmsgTrunc1(self):
         self.createAndSendFDs(1)
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTrunc2Int(self):
         # The cmsghdr structure has at least three members, two of
         # which are ints, so we still shouldn't see any ancillary
@@ -4371,6 +4376,7 @@ def _testCmsgTrunc2Int(self):
         self.createAndSendFDs(1)
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTruncLen0Minus1(self):
         self.checkTruncatedHeader(self.doRecvmsg(self.serv_sock, len(MSG),
                                                  socket.CMSG_LEN(0) - 1))
@@ -4408,6 +4414,7 @@ def checkTruncatedArray(self, ancbuf, maxdata, mindata=0):
         self.checkFDs(fds)
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTruncLen0(self):
         self.checkTruncatedArray(ancbuf=socket.CMSG_LEN(0), maxdata=0)
 
@@ -4416,6 +4423,7 @@ def _testCmsgTruncLen0(self):
         self.createAndSendFDs(1)
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTruncLen0Plus1(self):
         self.checkTruncatedArray(ancbuf=socket.CMSG_LEN(0) + 1, maxdata=1)
 
@@ -4424,6 +4432,7 @@ def _testCmsgTruncLen0Plus1(self):
         self.createAndSendFDs(2)
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTruncLen1(self):
         self.checkTruncatedArray(ancbuf=socket.CMSG_LEN(SIZEOF_INT),
                                  maxdata=SIZEOF_INT)
@@ -4434,6 +4443,7 @@ def _testCmsgTruncLen1(self):
 
 
     @skipForRefleakHuntinIf(sys.platform == "darwin", "#80931")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testCmsgTruncLen2Minus1(self):
         self.checkTruncatedArray(ancbuf=socket.CMSG_LEN(2 * SIZEOF_INT) - 1,
                                  maxdata=(2 * SIZEOF_INT) - 1)
@@ -4706,6 +4716,7 @@ def _testSingleCmsgTrunc0(self):
     # (but still too small) buffer sizes.
 
     @requireAttrs(socket, "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSingleCmsgTrunc1(self):
         self.checkHopLimitTruncatedHeader(ancbufsize=1)
 
@@ -4715,6 +4726,7 @@ def _testSingleCmsgTrunc1(self):
         self.sendToServer(MSG)
 
     @requireAttrs(socket, "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSingleCmsgTrunc2Int(self):
         self.checkHopLimitTruncatedHeader(ancbufsize=2 * SIZEOF_INT)
 
@@ -4724,6 +4736,7 @@ def _testSingleCmsgTrunc2Int(self):
         self.sendToServer(MSG)
 
     @requireAttrs(socket, "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSingleCmsgTruncLen0Minus1(self):
         self.checkHopLimitTruncatedHeader(ancbufsize=socket.CMSG_LEN(0) - 1)
 
@@ -4733,6 +4746,7 @@ def _testSingleCmsgTruncLen0Minus1(self):
         self.sendToServer(MSG)
 
     @requireAttrs(socket, "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSingleCmsgTruncInData(self):
         # Test truncation of a control message inside its associated
         # data.  The message may be returned with its data truncated,
@@ -4805,6 +4819,7 @@ def _testSecondCmsgTrunc0(self):
 
     @requireAttrs(socket, "CMSG_SPACE", "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT",
                   "IPV6_RECVTCLASS", "IPV6_TCLASS")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSecondCmsgTrunc1(self):
         self.checkTruncatedSecondHeader(socket.CMSG_SPACE(SIZEOF_INT) + 1)
 
@@ -4815,6 +4830,7 @@ def _testSecondCmsgTrunc1(self):
 
     @requireAttrs(socket, "CMSG_SPACE", "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT",
                   "IPV6_RECVTCLASS", "IPV6_TCLASS")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSecondCmsgTrunc2Int(self):
         self.checkTruncatedSecondHeader(socket.CMSG_SPACE(SIZEOF_INT) +
                                         2 * SIZEOF_INT)
@@ -4826,6 +4842,7 @@ def _testSecondCmsgTrunc2Int(self):
 
     @requireAttrs(socket, "CMSG_SPACE", "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT",
                   "IPV6_RECVTCLASS", "IPV6_TCLASS")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSecondCmsgTruncLen0Minus1(self):
         self.checkTruncatedSecondHeader(socket.CMSG_SPACE(SIZEOF_INT) +
                                         socket.CMSG_LEN(0) - 1)
@@ -4837,6 +4854,7 @@ def _testSecondCmsgTruncLen0Minus1(self):
 
     @requireAttrs(socket, "CMSG_SPACE", "IPV6_RECVHOPLIMIT", "IPV6_HOPLIMIT",
                   "IPV6_RECVTCLASS", "IPV6_TCLASS")
+    @unittest.skipIf(CMSG_TRUNC_RAISES_EMSGSIZE, "skipping, see gh-154240")
     def testSecondCmsgTruncInData(self):
         # Test truncation of the second of two control messages inside
         # its associated data.