diff --git a/io/tst-lchmod.c b/io/tst-lchmod.c
index 73e45549af..33ca474b50 100644
--- a/io/tst-lchmod.c
+++ b/io/tst-lchmod.c
@@ -102,68 +102,39 @@ test_1 (bool do_relative_path, int (*chmod_func) (int fd, const char *, mode_t,
   TEST_VERIFY ((st.st_mode & 0777) != 2);
   mode_t original_symlink_mode = st.st_mode;
 
-  /* Set to true if AT_SYMLINK_NOFOLLOW is supported.  */
-  bool nofollow;
-
   /* We should be able to change the mode of a file, including through
      the symbolic link to-file.  */
   const char *arg = select_path (do_relative_path, path_file, "file");
   TEST_COMPARE (chmod_func (fd, arg, 1, 0), 0);
   xstat (path_file, &st);
   TEST_COMPARE (st.st_mode & 0777, 1);
-  int ret = chmod_func (fd, path_file, 2, AT_SYMLINK_NOFOLLOW);
-  if (ret == 0)
-    {
-      printf ("info: AT_SYMLINK_NOFOLLOW support in %s\n", tempdir);
-      nofollow = true;
-    }
-  else
-    {
-      printf ("info: no AT_SYMLINK_NOFOLLOW support in %s\n", tempdir);
-      nofollow = false;
-
-      /* Set up things for the code below.  */
-      TEST_COMPARE (chmod_func (fd, path_file, 2, 0), 0);
-    }
+  arg = select_path (do_relative_path, path_to_file, "to-file");
+  TEST_COMPARE (chmod_func (fd, arg, 2, 0), 0);
   xstat (path_file, &st);
   TEST_COMPARE (st.st_mode & 0777, 2);
-  arg = select_path (do_relative_path, path_to_file, "to-file");
-  TEST_COMPARE (chmod_func (fd, path_to_file, 1, 0), 0);
+  xlstat (path_to_file, &st);
+  TEST_COMPARE (original_symlink_mode, st.st_mode);
+  arg = select_path (do_relative_path, path_file, "file");
+  TEST_COMPARE (chmod_func (fd, arg, 1, 0), 0);
   xstat (path_file, &st);
   TEST_COMPARE (st.st_mode & 0777, 1);
   xlstat (path_to_file, &st);
   TEST_COMPARE (original_symlink_mode, st.st_mode);
 
-  /* Changing the mode of a symbolic link may fail.  */
+  /* Changing the mode of a symbolic link should fail.  */
   arg = select_path (do_relative_path, path_to_file, "to-file");
-  ret = chmod_func (fd, arg, 2, AT_SYMLINK_NOFOLLOW);
-  if (nofollow)
-    {
-      TEST_COMPARE (ret, 0);
-
-      /* The mode of the link changed.  */
-      xlstat (path_to_file, &st);
-      TEST_COMPARE (st.st_mode & 0777, 2);
-
-      /* But the mode of the file is unchanged.  */
-      xstat (path_file, &st);
-      TEST_COMPARE (st.st_mode & 0777, 1);
+  int ret = chmod_func (fd, arg, 2, AT_SYMLINK_NOFOLLOW);
+  TEST_COMPARE (ret, -1);
+  TEST_COMPARE (errno, EOPNOTSUPP);
 
-    }
-  else
-    {
-      TEST_COMPARE (ret, -1);
-      TEST_COMPARE (errno, EOPNOTSUPP);
-
-      /* The modes should remain unchanged.  */
-      xstat (path_file, &st);
-      TEST_COMPARE (st.st_mode & 0777, 1);
-      xlstat (path_to_file, &st);
-      TEST_COMPARE (original_symlink_mode, st.st_mode);
-    }
+  /* The modes should remain unchanged.  */
+  xstat (path_file, &st);
+  TEST_COMPARE (st.st_mode & 0777, 1);
+  xlstat (path_to_file, &st);
+  TEST_COMPARE (original_symlink_mode, st.st_mode);
 
-  /* If we have NOFOLLOW support, we should be able to change the mode
-     of a dangling symbolic link or a symbolic link loop.  */
+  /* Likewise, changing dangling and looping symbolic links must
+     fail.  */
   const char *paths[] = { path_dangling, path_loop };
   for (size_t i = 0; i < array_length (paths); ++i)
     {
@@ -178,19 +149,10 @@ test_1 (bool do_relative_path, int (*chmod_func) (int fd, const char *, mode_t,
       original_symlink_mode = st.st_mode;
       arg = select_path (do_relative_path, path, filename);
       ret = chmod_func (fd, arg, new_mode, AT_SYMLINK_NOFOLLOW);
-      if (nofollow)
-        {
-          TEST_COMPARE (ret, 0);
-          xlstat (path, &st);
-          TEST_COMPARE (st.st_mode & 0777, new_mode);
-        }
-      else /* !nofollow.  */
-        {
-          TEST_COMPARE (ret, -1);
-          TEST_COMPARE (errno, EOPNOTSUPP);
-          xlstat (path, &st);
-          TEST_COMPARE (st.st_mode, original_symlink_mode);
-        }
+      TEST_COMPARE (ret, -1);
+      TEST_COMPARE (errno, EOPNOTSUPP);
+      xlstat (path, &st);
+      TEST_COMPARE (st.st_mode, original_symlink_mode);
     }
 
    /* A missing file should always result in ENOENT.  The presence of
diff --git a/sysdeps/unix/sysv/linux/fchmodat.c b/sysdeps/unix/sysv/linux/fchmodat.c
index 719053b333..17eca54051 100644
--- a/sysdeps/unix/sysv/linux/fchmodat.c
+++ b/sysdeps/unix/sysv/linux/fchmodat.c
@@ -45,6 +45,30 @@ fchmodat (int fd, const char *file, mode_t mode, int flag)
 	   caller can treat them as temporary if necessary.  */
 	return pathfd;
 
+      /* Use fstatat because fstat does not work on O_PATH descriptors
+	 before Linux 3.6.  */
+      struct stat64 st;
+      if (fstatat64 (pathfd, "", &st, AT_EMPTY_PATH) != 0)
+	{
+	  __close_nocancel (pathfd);
+	  return -1;
+	}
+
+      /* Some Linux versions with some file systems can actually
+	 change symbolic link permissions via /proc, but this is not
+	 intentional, and it gives inconsistent results (e.g., error
+	 return despite mode change).  The expected behavior is that
+	 symbolic link modes cannot be changed at all, and this check
+	 enforces that.  */
+      if (S_ISLNK (st.st_mode))
+	{
+	  __close_nocancel (pathfd);
+	  __set_errno (EOPNOTSUPP);
+	  return -1;
+	}
+
+      /* For most file systems, fchmod does not operate on O_PATH
+	 descriptors, so go through /proc.  */
       char buf[32];
       if (__snprintf (buf, sizeof (buf), "/proc/self/fd/%d", pathfd) < 0)
 	{
@@ -54,10 +78,6 @@ fchmodat (int fd, const char *file, mode_t mode, int flag)
 	  return -1;
 	}
 
-      /* This operates directly on the symbolic link if it is one.
-	 /proc/self/fd files look like symbolic links, but they are
-	 not.  (fchmod and fchmodat do not work on O_PATH descriptors,
-	 similar to fstat before Linux 3.6.)  */
       int ret = __chmod (buf, mode);
       if (ret != 0)
 	{
