diff --git a/glnx-backports.h b/glnx-backports.h
index 9ec11e4cf..a0177ad99 100644
--- a/glnx-backports.h
+++ b/glnx-backports.h
@@ -82,6 +82,27 @@ g_clear_fd (int     *fd_ptr,
 }
 #endif
 
+/* This is part of the backport of g_autofd, but we define it
+ * unconditionally because it's also used to implement glnx_close_fd() */
+static inline void
+_glnx_clear_fd_ignore_error (int *fd_ptr)
+{
+  /* Don't overwrite thread-local errno if closing the fd fails */
+  int errsv = errno;
+
+  if (!g_clear_fd (fd_ptr, NULL))
+    {
+      /* Do nothing: we ignore all errors, except for EBADF which
+       * is a programming error, checked for by g_close(). */
+    }
+
+  errno = errsv;
+}
+
+#if !GLIB_CHECK_VERSION(2, 76, 0)
+#define g_autofd __attribute__((cleanup(_glnx_clear_fd_ignore_error)))
+#endif
+
 #if !GLIB_CHECK_VERSION(2, 40, 0)
 #define g_info(...) g_log (G_LOG_DOMAIN, G_LOG_LEVEL_INFO, __VA_ARGS__)
 #endif
diff --git a/glnx-local-alloc.h b/glnx-local-alloc.h
index a6e0e9b4f..9ac8a027d 100644
--- a/glnx-local-alloc.h
+++ b/glnx-local-alloc.h
@@ -51,38 +51,23 @@ glnx_local_obj_unref (void *v)
  * glnx_close_fd:
  * @fdp: Pointer to fd
  *
- * Effectively `close (g_steal_fd (&fd))`.  Also
- * asserts that `close()` did not raise `EBADF` - encountering
- * that error is usually a critical bug in the program.
+ * Same as `g_clear_fd()`, but ignoring the error (if any) and making sure
+ * not to alter `errno`. As a result, this function can be used for cleanup
+ * in contexts where `errno` needs to be preserved.
  */
-static inline void
-glnx_close_fd (int *fdp)
-{
-  int errsv;
-
-  g_assert (fdp);
-
-  int fd = g_steal_fd (fdp);
-  if (fd >= 0)
-    {
-      errsv = errno;
-      if (close (fd) < 0)
-        g_assert (errno != EBADF);
-      errno = errsv;
-    }
-}
+#define glnx_close_fd _glnx_clear_fd_ignore_error
 
 /**
  * glnx_fd_close:
  *
- * Deprecated in favor of `glnx_autofd`.
+ * Deprecated in favor of `g_autofd`.
  */
-#define glnx_fd_close __attribute__((cleanup(glnx_close_fd)))
+#define glnx_fd_close g_autofd
 /**
  * glnx_autofd:
  *
- * Call close() on a variable location when it goes out of scope.
+ * Deprecated in favor of `g_autofd`.
  */
-#define glnx_autofd __attribute__((cleanup(glnx_close_fd)))
+#define glnx_autofd g_autofd
 
 G_END_DECLS