diff --git a/glib/gspawn.c b/glib/gspawn.c
index 8bbe573f7..2b48b5600 100644
--- a/glib/gspawn.c
+++ b/glib/gspawn.c
@@ -1258,13 +1258,13 @@ unset_cloexec (int fd)
 /* This function is called between fork() and exec() and hence must be
  * async-signal-safe (see signal-safety(7)). */
 static int
-dupfd_cloexec (int parent_fd)
+dupfd_cloexec (int old_fd, int new_fd_min)
 {
   int fd, errsv;
 #ifdef F_DUPFD_CLOEXEC
   do
     {
-      fd = fcntl (parent_fd, F_DUPFD_CLOEXEC, 3);
+      fd = fcntl (old_fd, F_DUPFD_CLOEXEC, new_fd_min);
       errsv = errno;
     }
   while (fd == -1 && errsv == EINTR);
@@ -1275,7 +1275,7 @@ dupfd_cloexec (int parent_fd)
   int result, flags;
   do
     {
-      fd = fcntl (parent_fd, F_DUPFD, 3);
+      fd = fcntl (old_fd, F_DUPFD, new_fd_min);
       errsv = errno;
     }
   while (fd == -1 && errsv == EINTR);
@@ -1563,6 +1563,7 @@ do_exec (gint                  child_err_report_fd,
          gpointer              user_data)
 {
   gsize i;
+  gint max_target_fd = 0;
 
   if (working_directory && chdir (working_directory) < 0)
     write_err_and_exit (child_err_report_fd,
@@ -1661,39 +1662,45 @@ do_exec (gint                  child_err_report_fd,
   /*
    * Work through the @source_fds and @target_fds mapping.
    *
-   * Based on code derived from
+   * Based on code originally derived from
    * gnome-terminal:src/terminal-screen.c:terminal_screen_child_setup(),
-   * used under the LGPLv2+ with permission from author.
+   * used under the LGPLv2+ with permission from author. (The code has
+   * since migrated to vte:src/spawn.cc:SpawnContext::exec and is no longer
+   * terribly similar to what we have here.)
    */
 
-  /* Basic fd assignments (where source == target) we can just unset FD_CLOEXEC
-   *
-   * If we're doing remapping fd assignments, we need to handle
-   * the case where the user has specified e.g.:
-   * 5 -> 4, 4 -> 6
-   *
-   * We do this by duping the source fds temporarily in a first pass.
-   *
-   * If any of the @target_fds conflict with @child_err_report_fd, dup the
-   * latter so it doesn’t get conflated.
-   */
   if (n_fds > 0)
     {
       for (i = 0; i < n_fds; i++)
-        {
-          if (source_fds[i] != target_fds[i])
-            source_fds[i] = dupfd_cloexec (source_fds[i]);
-        }
+        max_target_fd = MAX (max_target_fd, target_fds[i]);
+
+      /* If we're doing remapping fd assignments, we need to handle
+       * the case where the user has specified e.g. 5 -> 4, 4 -> 6.
+       * We do this by duping all source fds, taking care to ensure the new
+       * fds are larger than any target fd to avoid introducing new conflicts.
+       */
       for (i = 0; i < n_fds; i++)
         {
+          if (source_fds[i] != target_fds[i])
+            source_fds[i] = dupfd_cloexec (source_fds[i], max_target_fd + 1);
+        }
+
+      for (i = 0; i < n_fds; i++)
+        {
+          /* For basic fd assignments (where source == target), we can just
+           * unset FD_CLOEXEC.
+           */
           if (source_fds[i] == target_fds[i])
             {
               unset_cloexec (source_fds[i]);
             }
           else
             {
+              /* If any of the @target_fds conflict with @child_err_report_fd,
+               * dup it so it doesn’t get conflated.
+               */
               if (target_fds[i] == child_err_report_fd)
-                child_err_report_fd = dupfd_cloexec (child_err_report_fd);
+                child_err_report_fd = dupfd_cloexec (child_err_report_fd, max_target_fd + 1);
 
               safe_dup2 (source_fds[i], target_fds[i]);
               close_and_invalidate (&source_fds[i]);