diff --git a/winsup/cygwin/dir.cc b/winsup/cygwin/dir.cc
index 29a9dfa83..3429fe022 100644
--- a/winsup/cygwin/dir.cc
+++ b/winsup/cygwin/dir.cc
@@ -313,15 +313,27 @@ mkdir (const char *dir, mode_t mode)
       /* Following Linux, and intentionally ignoring POSIX, do not
 	 resolve the last component of DIR if it is a symlink, even if
 	 DIR has a trailing slash.  Achieve this by stripping trailing
-	 slashes or backslashes.  */
+	 slashes or backslashes.
+
+	 Exception: If DIR == 'x:' followed by one or more slashes or
+	 backslashes, and if there's at least one backslash, assume
+	 that the user is referring to the root directory of drive x.
+	 Retain one backslash in this case.  */
       if (isdirsep (dir[strlen (dir) - 1]))
 	{
 	  /* This converts // to /, but since both give EEXIST, we're okay.  */
 	  char *buf;
 	  char *p = stpcpy (buf = tp.c_get (), dir) - 1;
+	  bool msdos = false;
 	  dir = buf;
 	  while (p > dir && isdirsep (*p))
-	    *p-- = '\0';
+	    {
+	      if (*p == '\\')
+		msdos = true;
+	      *p-- = '\0';
+	    }
+	  if (msdos && p == dir + 1 && isdrive (dir))
+	    p[1] = '\\';
 	}
       if (!(fh = build_fh_name (dir, PC_SYM_NOFOLLOW)))
 	__leave;   /* errno already set */;
@@ -360,20 +372,31 @@ rmdir (const char *dir)
 	  set_errno (ENOENT);
 	  __leave;
 	}
-
       /* Following Linux, and intentionally ignoring POSIX, do not
 	 resolve the last component of DIR if it is a symlink, even if
 	 DIR has a trailing slash.  Achieve this by stripping trailing
-	 slashes or backslashes.  */
+	 slashes or backslashes.
+
+	 Exception: If DIR == 'x:' followed by one or more slashes or
+	 backslashes, and if there's at least one backslash, assume
+	 that the user is referring to the root directory of drive x.
+	 Retain one backslash in this case.  */
       if (isdirsep (dir[strlen (dir) - 1]))
 	{
 	  /* This converts // to /, but since both give ENOTEMPTY,
 	     we're okay.  */
 	  char *buf;
 	  char *p = stpcpy (buf = tp.c_get (), dir) - 1;
+	  bool msdos = false;
 	  dir = buf;
 	  while (p > dir && isdirsep (*p))
-	    *p-- = '\0';
+	    {
+	      if (*p == '\\')
+		msdos = true;
+	      *p-- = '\0';
+	    }
+	  if (msdos && p == dir + 1 && isdrive (dir))
+	    p[1] = '\\';
 	}
       if (!(fh = build_fh_name (dir, PC_SYM_NOFOLLOW)))
 	__leave;   /* errno already set */;
diff --git a/winsup/cygwin/release/3.1.0 b/winsup/cygwin/release/3.1.0
index f3abff10f..3f2f3c86b 100644
--- a/winsup/cygwin/release/3.1.0
+++ b/winsup/cygwin/release/3.1.0
@@ -87,3 +87,7 @@ Bug Fixes
 
 - Fix an assertion failure on an invalid path.
   Addresses: https://cygwin.com/ml/cygwin/2019-09/msg00228.html
+
+- If the argument to mkdir(2) or rmdir(2) is 'x:\', don't strip the
+  trailing backslash.
+  Addresses: https://cygwin.com/ml/cygwin/2019-08/msg00334.html