diff --git a/elf/dl-close.c b/elf/dl-close.c
index 73b2817bbf..3d52126200 100644
--- a/elf/dl-close.c
+++ b/elf/dl-close.c
@@ -164,8 +164,6 @@ _dl_close_worker (struct link_map *map, bool force)
 
   bool any_tls = false;
   const unsigned int nloaded = ns->_ns_nloaded;
-  char used[nloaded];
-  char done[nloaded];
   struct link_map *maps[nloaded];
 
   /* Run over the list and assign indexes to the link maps and enter
@@ -173,24 +171,21 @@ _dl_close_worker (struct link_map *map, bool force)
   int idx = 0;
   for (struct link_map *l = ns->_ns_loaded; l != NULL; l = l->l_next)
     {
+      l->l_map_used = 0;
+      l->l_map_done = 0;
       l->l_idx = idx;
       maps[idx] = l;
       ++idx;
-
     }
   assert (idx == nloaded);
 
-  /* Prepare the bitmaps.  */
-  memset (used, '\0', sizeof (used));
-  memset (done, '\0', sizeof (done));
-
   /* Keep track of the lowest index link map we have covered already.  */
   int done_index = -1;
   while (++done_index < nloaded)
     {
       struct link_map *l = maps[done_index];
 
-      if (done[done_index])
+      if (l->l_map_done)
 	/* Already handled.  */
 	continue;
 
@@ -201,12 +196,12 @@ _dl_close_worker (struct link_map *map, bool force)
 	  /* See CONCURRENCY NOTES in cxa_thread_atexit_impl.c to know why
 	     acquire is sufficient and correct.  */
 	  && atomic_load_acquire (&l->l_tls_dtor_count) == 0
-	  && !used[done_index])
+	  && !l->l_map_used)
 	continue;
 
       /* We need this object and we handle it now.  */
-      done[done_index] = 1;
-      used[done_index] = 1;
+      l->l_map_used = 1;
+      l->l_map_done = 1;
       /* Signal the object is still needed.  */
       l->l_idx = IDX_STILL_USED;
 
@@ -222,9 +217,9 @@ _dl_close_worker (struct link_map *map, bool force)
 		{
 		  assert ((*lp)->l_idx >= 0 && (*lp)->l_idx < nloaded);
 
-		  if (!used[(*lp)->l_idx])
+		  if (!(*lp)->l_map_used)
 		    {
-		      used[(*lp)->l_idx] = 1;
+		      (*lp)->l_map_used = 1;
 		      /* If we marked a new object as used, and we've
 			 already processed it, then we need to go back
 			 and process again from that point forward to
@@ -247,9 +242,9 @@ _dl_close_worker (struct link_map *map, bool force)
 	      {
 		assert (jmap->l_idx >= 0 && jmap->l_idx < nloaded);
 
-		if (!used[jmap->l_idx])
+		if (!jmap->l_map_used)
 		  {
-		    used[jmap->l_idx] = 1;
+		    jmap->l_map_used = 1;
 		    if (jmap->l_idx - 1 < done_index)
 		      done_index = jmap->l_idx - 1;
 		  }
@@ -259,8 +254,7 @@ _dl_close_worker (struct link_map *map, bool force)
 
   /* Sort the entries.  We can skip looking for the binary itself which is
      at the front of the search list for the main namespace.  */
-  _dl_sort_maps (maps + (nsid == LM_ID_BASE), nloaded - (nsid == LM_ID_BASE),
-		 used + (nsid == LM_ID_BASE), true);
+  _dl_sort_maps (maps, nloaded, (nsid == LM_ID_BASE), true);
 
   /* Call all termination functions at once.  */
 #ifdef SHARED
@@ -277,7 +271,7 @@ _dl_close_worker (struct link_map *map, bool force)
       /* All elements must be in the same namespace.  */
       assert (imap->l_ns == nsid);
 
-      if (!used[i])
+      if (!imap->l_map_used)
 	{
 	  assert (imap->l_type == lt_loaded && !imap->l_nodelete_active);
 
@@ -330,7 +324,7 @@ _dl_close_worker (struct link_map *map, bool force)
 	  if (i < first_loaded)
 	    first_loaded = i;
 	}
-      /* Else used[i].  */
+      /* Else imap->l_map_used.  */
       else if (imap->l_type == lt_loaded)
 	{
 	  struct r_scope_elem *new_list = NULL;
@@ -554,7 +548,7 @@ _dl_close_worker (struct link_map *map, bool force)
   for (unsigned int i = first_loaded; i < nloaded; ++i)
     {
       struct link_map *imap = maps[i];
-      if (!used[i])
+      if (!imap->l_map_used)
 	{
 	  assert (imap->l_type == lt_loaded);
 
diff --git a/elf/dl-deps.c b/elf/dl-deps.c
index b5a43232a7..0851971dca 100644
--- a/elf/dl-deps.c
+++ b/elf/dl-deps.c
@@ -611,7 +611,7 @@ Filters not supported with LD_TRACE_PRELINKING"));
     memcpy (l_initfini, map->l_searchlist.r_list,
 	    nlist * sizeof (struct link_map *));
 
-  _dl_sort_maps (&l_initfini[1], nlist - 1, NULL, false);
+  _dl_sort_maps (l_initfini, nlist, 1, false);
 
   /* Terminate the list of dependencies.  */
   l_initfini[nlist] = NULL;
diff --git a/elf/dl-fini.c b/elf/dl-fini.c
index 231db3d66d..5b1bf6371c 100644
--- a/elf/dl-fini.c
+++ b/elf/dl-fini.c
@@ -92,8 +92,7 @@ _dl_fini (void)
 	  /* Now we have to do the sorting.  We can skip looking for the
 	     binary itself which is at the front of the search list for
 	     the main namespace.  */
-	  _dl_sort_maps (maps + (ns == LM_ID_BASE), nmaps - (ns == LM_ID_BASE),
-			 NULL, true);
+	  _dl_sort_maps (maps, nmaps, (ns == LM_ID_BASE), true);
 
 	  /* We do not rely on the linked list of loaded object anymore
 	     from this point on.  We have our own list here (maps).  The
diff --git a/elf/dl-sort-maps.c b/elf/dl-sort-maps.c
index 86f1e23c85..7d143cc487 100644
--- a/elf/dl-sort-maps.c
+++ b/elf/dl-sort-maps.c
@@ -16,16 +16,24 @@
    License along with the GNU C Library; if not, see
    <https://www.gnu.org/licenses/>.  */
 
+#include <assert.h>
 #include <ldsodefs.h>
+#include <elf/dl-tunables.h>
 
+/* Note: this is the older, "original" sorting algorithm, being used as
+   default up to 2.32.
 
-/* Sort array MAPS according to dependencies of the contained objects.
-   Array USED, if non-NULL, is permutated along MAPS.  If FOR_FINI this is
-   called for finishing an object.  */
-void
-_dl_sort_maps (struct link_map **maps, unsigned int nmaps, char *used,
-	       bool for_fini)
+   Sort array MAPS according to dependencies of the contained objects.
+   If FOR_FINI is true, this is called for finishing an object.  */
+static void
+_dl_sort_maps_original (struct link_map **maps, unsigned int nmaps,
+			unsigned int skip, bool for_fini)
 {
+  /* Allows caller to do the common optimization of skipping the first map,
+     usually the main binary.  */
+  maps += skip;
+  nmaps -= skip;
+
   /* A list of one element need not be sorted.  */
   if (nmaps <= 1)
     return;
@@ -66,14 +74,6 @@ _dl_sort_maps (struct link_map **maps, unsigned int nmaps, char *used,
 			   (k - i) * sizeof (maps[0]));
 		  maps[k] = thisp;
 
-		  if (used != NULL)
-		    {
-		      char here_used = used[i];
-		      memmove (&used[i], &used[i + 1],
-			       (k - i) * sizeof (used[0]));
-		      used[k] = here_used;
-		    }
-
 		  if (seen[i + 1] > nmaps - i)
 		    {
 		      ++i;
@@ -120,3 +120,160 @@ _dl_sort_maps (struct link_map **maps, unsigned int nmaps, char *used,
     next:;
     }
 }
+
+#if !HAVE_TUNABLES
+/* In this case, just default to the original algorithm.  */
+strong_alias (_dl_sort_maps_original, _dl_sort_maps);
+#else
+
+/* We use a recursive function due to its better clarity and ease of
+   implementation, as well as faster execution speed. We already use
+   alloca() for list allocation during the breadth-first search of
+   dependencies in _dl_map_object_deps(), and this should be on the
+   same order of worst-case stack usage.  */
+
+static void
+dfs_traversal (struct link_map ***rpo, struct link_map *map,
+	       bool *do_reldeps)
+{
+  if (map->l_visited)
+    return;
+
+  map->l_visited = 1;
+
+  if (map->l_initfini)
+    {
+      for (int i = 0; map->l_initfini[i] != NULL; i++)
+	{
+	  struct link_map *dep = map->l_initfini[i];
+	  if (dep->l_visited == 0)
+	    dfs_traversal (rpo, dep, do_reldeps);
+	}
+    }
+
+  if (__glibc_unlikely (do_reldeps != NULL && map->l_reldeps != NULL))
+    {
+      /* Indicate that we encountered relocation dependencies during
+	 traversal.  */
+      *do_reldeps = true;
+
+      for (int m = map->l_reldeps->act - 1; m >= 0; m--)
+	{
+	  struct link_map *dep = map->l_reldeps->list[m];
+	  if (dep->l_visited == 0)
+	    dfs_traversal (rpo, dep, do_reldeps);
+	}
+    }
+
+  *rpo -= 1;
+  **rpo = map;
+}
+
+/* Topologically sort array MAPS according to dependencies of the contained
+   objects.  */
+
+static void
+_dl_sort_maps_dfs (struct link_map **maps, unsigned int nmaps,
+		   unsigned int skip __attribute__ ((unused)), bool for_fini)
+{
+  for (int i = 0; i < nmaps; i++)
+    maps[i]->l_visited = 0;
+
+  /* We apply DFS traversal for each of maps[i] until the whole total order
+     is found and we're at the start of the Reverse-Postorder (RPO) sequence,
+     which is a topological sort.
+
+     We go from maps[nmaps - 1] backwards towards maps[0] at this level.
+     Due to the breadth-first search (BFS) ordering we receive, going
+     backwards usually gives a more shallow depth-first recursion depth,
+     adding more stack usage safety. Also, combined with the natural
+     processing order of l_initfini[] at each node during DFS, this maintains
+     an ordering closer to the original link ordering in the sorting results
+     under most simpler cases.
+
+     Another reason we order the top level backwards, it that maps[0] is
+     usually exactly the main object of which we're in the midst of
+     _dl_map_object_deps() processing, and maps[0]->l_initfini[] is still
+     blank. If we start the traversal from maps[0], since having no
+     dependencies yet filled in, maps[0] will always be immediately
+     incorrectly placed at the last place in the order (first in reverse).
+     Adjusting the order so that maps[0] is last traversed naturally avoids
+     this problem.
+
+     Further, the old "optimization" of skipping the main object at maps[0]
+     from the call-site (i.e. _dl_sort_maps(maps+1,nmaps-1)) is in general
+     no longer valid, since traversing along object dependency-links
+     may "find" the main object even when it is not included in the initial
+     order (e.g. a dlopen()'ed shared object can have circular dependencies
+     linked back to itself). In such a case, traversing N-1 objects will
+     create a N-object result, and raise problems.
+
+     To summarize, just passing in the full list, and iterating from back
+     to front makes things much more straightforward.  */
+
+  struct link_map *rpo[nmaps];
+  struct link_map **rpo_head = &rpo[nmaps];
+
+  bool do_reldeps = false;
+  bool *do_reldeps_ref = (for_fini ? &do_reldeps : NULL);
+
+  for (int i = nmaps - 1; i >= 0; i--)
+    {
+      dfs_traversal (&rpo_head, maps[i], do_reldeps_ref);
+
+      /* We can break early if all objects are already placed.  */
+      if (rpo_head == rpo)
+	goto end;
+    }
+  assert (rpo_head == rpo);
+
+ end:
+  /* This is avoided if !FOR_FINI or if we didn't find any reldeps in
+     the first DFS traversal.  */
+  if (do_reldeps)
+    {
+      for (int i = 0; i < nmaps; i++)
+	rpo[i]->l_visited = 0;
+
+      struct link_map **maps_head = &maps[nmaps];
+      for (int i = nmaps - 1; i >= 0; i--)
+	{
+	  dfs_traversal (&maps_head, rpo[i], NULL);
+
+	  /* We can break early if all objects are already placed.
+	     The below memcpy is not needed in the do_reldeps case here,
+	     since we wrote back to maps[] during DFS traversal.  */
+	  if (maps_head == maps)
+	    return;
+	}
+      assert (maps_head == maps);
+      return;
+    }
+
+  memcpy (maps, rpo, sizeof (struct link_map *) * nmaps);
+}
+
+void
+_dl_sort_maps (struct link_map **maps, unsigned int nmaps,
+	       unsigned int skip, bool for_fini)
+{
+  /* Function pointer to sorting algorithm currently in use.  */
+  static void (*sort_maps) (struct link_map **, unsigned int,
+			    unsigned int, bool) = NULL;
+  if (__glibc_unlikely (sort_maps == NULL))
+    {
+      /* Select sorting algorithm based on tunable value.  */
+      int32_t algorithm = TUNABLE_GET (glibc, rtld, dynamic_sort,
+				       int32_t, NULL);
+      if (__glibc_likely (algorithm == 1))
+	sort_maps = _dl_sort_maps_original;
+      else if (algorithm == 2)
+	sort_maps = _dl_sort_maps_dfs;
+      else
+	__builtin_unreachable ();
+    }
+
+  sort_maps (maps, nmaps, skip, for_fini);
+}
+
+#endif /* HAVE_TUNABLES.  */
diff --git a/elf/dl-tunables.list b/elf/dl-tunables.list
index 0d398dd251..aeeafe704a 100644
--- a/elf/dl-tunables.list
+++ b/elf/dl-tunables.list
@@ -126,4 +126,13 @@ glibc {
       default: 3
     }
   }
+
+  rtld {
+    dynamic_sort {
+      type: INT_32
+      minval: 1
+      maxval: 2
+      default: 1
+    }
+  }
 }
diff --git a/include/link.h b/include/link.h
index aea268439c..48c11c5d68 100644
--- a/include/link.h
+++ b/include/link.h
@@ -177,6 +177,10 @@ struct link_map
     unsigned int l_init_called:1; /* Nonzero if DT_INIT function called.  */
     unsigned int l_global:1;	/* Nonzero if object in _dl_global_scope.  */
     unsigned int l_reserved:2;	/* Reserved for internal use.  */
+    unsigned int l_visited:1;   /* Used internally for map dependency
+				   graph traversal.  */
+    unsigned int l_map_used:1;  /* These two bits are used during traversal */
+    unsigned int l_map_done:1;  /* of maps in _dl_close_worker(). */
     unsigned int l_phdr_allocated:1; /* Nonzero if the data structure pointed
 					to by `l_phdr' is allocated.  */
     unsigned int l_soname_added:1; /* Nonzero if the SONAME is for sure in
diff --git a/sysdeps/generic/ldsodefs.h b/sysdeps/generic/ldsodefs.h
index 5ff4a2831b..a0f60df81c 100644
--- a/sysdeps/generic/ldsodefs.h
+++ b/sysdeps/generic/ldsodefs.h
@@ -1017,8 +1017,8 @@ extern void _dl_init (struct link_map *main_map, int argc, char **argv,
 extern void _dl_fini (void) attribute_hidden;
 
 /* Sort array MAPS according to dependencies of the contained objects.  */
-extern void _dl_sort_maps (struct link_map **maps, unsigned int nmaps,
-			   char *used, bool for_fini) attribute_hidden;
+extern void _dl_sort_maps (struct link_map **, unsigned int, unsigned int,
+			   bool) attribute_hidden;
 
 /* The dynamic linker calls this function before and having changing
    any shared object mappings.  The `r_state' member of `struct r_debug'
