diff --git a/NEWS b/NEWS
index 82e868d73b..fd9d34b9b4 100644
--- a/NEWS
+++ b/NEWS
@@ -64,6 +64,7 @@ The following bugs are resolved with this release:
   [30305] x86_64: Fix asm constraints in feraiseexcept
   [30477] libc: [RISCV]: time64 does not work on riscv32
   [30515] _dl_find_object incorrectly returns 1 during early startup
+  [30785] Always call destructors in reverse constructor order
 
 Version 2.36
 
diff --git a/elf/dl-close.c b/elf/dl-close.c
index 14deca2e2b..640bbd88c3 100644
--- a/elf/dl-close.c
+++ b/elf/dl-close.c
@@ -138,30 +138,31 @@ _dl_close_worker (struct link_map *map, bool force)
 
   bool any_tls = false;
   const unsigned int nloaded = ns->_ns_nloaded;
-  struct link_map *maps[nloaded];
 
-  /* Run over the list and assign indexes to the link maps and enter
-     them into the MAPS array.  */
+  /* Run over the list and assign indexes to the link maps.  */
   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);
 
-  /* Keep track of the lowest index link map we have covered already.  */
-  int done_index = -1;
-  while (++done_index < nloaded)
+  /* Keep marking link maps until no new link maps are found.  */
+  for (struct link_map *l = ns->_ns_loaded; l != NULL; )
     {
-      struct link_map *l = maps[done_index];
+      /* next is reset to earlier link maps for remarking.  */
+      struct link_map *next = l->l_next;
+      int next_idx = l->l_idx + 1; /* next->l_idx, but covers next == NULL.  */
 
       if (l->l_map_done)
-	/* Already handled.  */
-	continue;
+	{
+	  /* Already handled.  */
+	  l = next;
+	  continue;
+	}
 
       /* Check whether this object is still used.  */
       if (l->l_type == lt_loaded
@@ -171,7 +172,10 @@ _dl_close_worker (struct link_map *map, bool force)
 	     acquire is sufficient and correct.  */
 	  && atomic_load_acquire (&l->l_tls_dtor_count) == 0
 	  && !l->l_map_used)
-	continue;
+	{
+	  l = next;
+	  continue;
+	}
 
       /* We need this object and we handle it now.  */
       l->l_map_used = 1;
@@ -198,8 +202,11 @@ _dl_close_worker (struct link_map *map, bool force)
 			 already processed it, then we need to go back
 			 and process again from that point forward to
 			 ensure we keep all of its dependencies also.  */
-		      if ((*lp)->l_idx - 1 < done_index)
-			done_index = (*lp)->l_idx - 1;
+		      if ((*lp)->l_idx < next_idx)
+			{
+			  next = *lp;
+			  next_idx = next->l_idx;
+			}
 		    }
 		}
 
@@ -219,44 +226,65 @@ _dl_close_worker (struct link_map *map, bool force)
 		if (!jmap->l_map_used)
 		  {
 		    jmap->l_map_used = 1;
-		    if (jmap->l_idx - 1 < done_index)
-		      done_index = jmap->l_idx - 1;
+		    if (jmap->l_idx < next_idx)
+		      {
+			  next = jmap;
+			  next_idx = next->l_idx;
+		      }
 		  }
 	      }
 	  }
+
+      l = next;
     }
 
-  /* 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, nloaded, (nsid == LM_ID_BASE), true);
-
-  /* Call all termination functions at once.  */
-  bool unload_any = false;
-  bool scope_mem_left = false;
-  unsigned int unload_global = 0;
-  unsigned int first_loaded = ~0;
-  for (unsigned int i = 0; i < nloaded; ++i)
+  /* Call the destructors in reverse constructor order, and remove the
+     closed link maps from the list.  */
+  for (struct link_map **init_called_head = &_dl_init_called_list;
+       *init_called_head != NULL; )
     {
-      struct link_map *imap = maps[i];
+      struct link_map *imap = *init_called_head;
 
-      /* All elements must be in the same namespace.  */
-      assert (imap->l_ns == nsid);
-
-      if (!imap->l_map_used)
+      /* _dl_init_called_list is global, to produce a global odering.
+	 Ignore the other namespaces (and link maps that are still used).  */
+      if (imap->l_ns != nsid || imap->l_map_used)
+	init_called_head = &imap->l_init_called_next;
+      else
 	{
 	  assert (imap->l_type == lt_loaded && !imap->l_nodelete_active);
 
-	  /* Call its termination function.  Do not do it for
-	     half-cooked objects.  Temporarily disable exception
-	     handling, so that errors are fatal.  */
-	  if (imap->l_init_called)
+	  /* _dl_init_called_list is updated at the same time as
+	     l_init_called.  */
+	  assert (imap->l_init_called);
+
+	  if (imap->l_info[DT_FINI_ARRAY] != NULL
+	      || imap->l_info[DT_FINI] != NULL)
 	    _dl_catch_exception (NULL, _dl_call_fini, imap);
 
 #ifdef SHARED
 	  /* Auditing checkpoint: we remove an object.  */
 	  _dl_audit_objclose (imap);
 #endif
+	  /* Unlink this link map.  */
+	  *init_called_head = imap->l_init_called_next;
+	}
+    }
 
+
+  bool unload_any = false;
+  bool scope_mem_left = false;
+  unsigned int unload_global = 0;
+
+  /* For skipping un-unloadable link maps in the second loop.  */
+  struct link_map *first_loaded = ns->_ns_loaded;
+
+  /* Iterate over the namespace to find objects to unload.  Some
+     unloadable objects may not be on _dl_init_called_list due to
+     dlopen failure.  */
+  for (struct link_map *imap = first_loaded; imap != NULL; imap = imap->l_next)
+    {
+      if (!imap->l_map_used)
+	{
 	  /* This object must not be used anymore.  */
 	  imap->l_removed = 1;
 
@@ -267,8 +295,8 @@ _dl_close_worker (struct link_map *map, bool force)
 	    ++unload_global;
 
 	  /* Remember where the first dynamically loaded object is.  */
-	  if (i < first_loaded)
-	    first_loaded = i;
+	  if (first_loaded == NULL)
+	      first_loaded = imap;
 	}
       /* Else imap->l_map_used.  */
       else if (imap->l_type == lt_loaded)
@@ -404,8 +432,8 @@ _dl_close_worker (struct link_map *map, bool force)
 	    imap->l_loader = NULL;
 
 	  /* Remember where the first dynamically loaded object is.  */
-	  if (i < first_loaded)
-	    first_loaded = i;
+	  if (first_loaded == NULL)
+	      first_loaded = imap;
 	}
     }
 
@@ -476,10 +504,11 @@ _dl_close_worker (struct link_map *map, bool force)
 
   /* Check each element of the search list to see if all references to
      it are gone.  */
-  for (unsigned int i = first_loaded; i < nloaded; ++i)
+  for (struct link_map *imap = first_loaded; imap != NULL; )
     {
-      struct link_map *imap = maps[i];
-      if (!imap->l_map_used)
+      if (imap->l_map_used)
+	imap = imap->l_next;
+      else
 	{
 	  assert (imap->l_type == lt_loaded);
 
@@ -690,7 +719,9 @@ _dl_close_worker (struct link_map *map, bool force)
 	  if (imap == GL(dl_initfirst))
 	    GL(dl_initfirst) = NULL;
 
+	  struct link_map *next = imap->l_next;
 	  free (imap);
+	  imap = next;
 	}
     }
 
diff --git a/elf/dl-fini.c b/elf/dl-fini.c
index 50ff94db16..50087a1bfc 100644
--- a/elf/dl-fini.c
+++ b/elf/dl-fini.c
@@ -24,116 +24,68 @@
 void
 _dl_fini (void)
 {
-  /* Lots of fun ahead.  We have to call the destructors for all still
-     loaded objects, in all namespaces.  The problem is that the ELF
-     specification now demands that dependencies between the modules
-     are taken into account.  I.e., the destructor for a module is
-     called before the ones for any of its dependencies.
+  /* Call destructors strictly in the reverse order of constructors.
+     This causes fewer surprises than some arbitrary reordering based
+     on new (relocation) dependencies.  None of the objects are
+     unmapped, so applications can deal with this if their DSOs remain
+     in a consistent state after destructors have run.  */
 
-     To make things more complicated, we cannot simply use the reverse
-     order of the constructors.  Since the user might have loaded objects
-     using `dlopen' there are possibly several other modules with its
-     dependencies to be taken into account.  Therefore we have to start
-     determining the order of the modules once again from the beginning.  */
+  /* Protect against concurrent loads and unloads.  */
+  __rtld_lock_lock_recursive (GL(dl_load_lock));
 
-  /* We run the destructors of the main namespaces last.  As for the
-     other namespaces, we pick run the destructors in them in reverse
-     order of the namespace ID.  */
+  /* Ignore objects which are opened during shutdown.  */
+  struct link_map *local_init_called_list = _dl_init_called_list;
+
+  for (struct link_map *l = local_init_called_list; l != NULL;
+       l = l->l_init_called_next)
+      /* Bump l_direct_opencount of all objects so that they
+	 are not dlclose()ed from underneath us.  */
+      ++l->l_direct_opencount;
+
+  /* After this point, everything linked from local_init_called_list
+     cannot be unloaded because of the reference counter update.  */
+  __rtld_lock_unlock_recursive (GL(dl_load_lock));
+
+  /* Perform two passes: One for non-audit modules, one for audit
+     modules.  This way, audit modules receive unload notifications
+     for non-audit objects, and the destructors for audit modules
+     still run.  */
 #ifdef SHARED
-  int do_audit = 0;
- again:
+  int last_pass = GLRO(dl_naudit) > 0;
+  Lmid_t last_ns = -1;
+  for (int do_audit = 0; do_audit <= last_pass; ++do_audit)
 #endif
-  for (Lmid_t ns = GL(dl_nns) - 1; ns >= 0; --ns)
-    {
-      /* Protect against concurrent loads and unloads.  */
-      __rtld_lock_lock_recursive (GL(dl_load_lock));
+    for (struct link_map *l = local_init_called_list; l != NULL;
+	 l = l->l_init_called_next)
+      {
+#ifdef SHARED
+	if (GL(dl_ns)[l->l_ns]._ns_loaded->l_auditing != do_audit)
+	  continue;
 
-      unsigned int nloaded = GL(dl_ns)[ns]._ns_nloaded;
-      /* No need to do anything for empty namespaces or those used for
-	 auditing DSOs.  */
-      if (nloaded == 0
-#ifdef SHARED
-	  || GL(dl_ns)[ns]._ns_loaded->l_auditing != do_audit
-#endif
-	  )
-	__rtld_lock_unlock_recursive (GL(dl_load_lock));
-      else
-	{
-#ifdef SHARED
-	  _dl_audit_activity_nsid (ns, LA_ACT_DELETE);
+	/* Avoid back-to-back calls of _dl_audit_activity_nsid for the
+	   same namespace.  */
+	if (last_ns != l->l_ns)
+	  {
+	    if (last_ns >= 0)
+	      _dl_audit_activity_nsid (last_ns, LA_ACT_CONSISTENT);
+	    _dl_audit_activity_nsid (l->l_ns, LA_ACT_DELETE);
+	    last_ns = l->l_ns;
+	  }
 #endif
 
-	  /* Now we can allocate an array to hold all the pointers and
-	     copy the pointers in.  */
-	  struct link_map *maps[nloaded];
+	/* There is no need to re-enable exceptions because _dl_fini
+	   is not called from a context where exceptions are caught.  */
+	_dl_call_fini (l);
 
-	  unsigned int i;
-	  struct link_map *l;
-	  assert (nloaded != 0 || GL(dl_ns)[ns]._ns_loaded == NULL);
-	  for (l = GL(dl_ns)[ns]._ns_loaded, i = 0; l != NULL; l = l->l_next)
-	    /* Do not handle ld.so in secondary namespaces.  */
-	    if (l == l->l_real)
-	      {
-		assert (i < nloaded);
-
-		maps[i] = l;
-		l->l_idx = i;
-		++i;
-
-		/* Bump l_direct_opencount of all objects so that they
-		   are not dlclose()ed from underneath us.  */
-		++l->l_direct_opencount;
-	      }
-	  assert (ns != LM_ID_BASE || i == nloaded);
-	  assert (ns == LM_ID_BASE || i == nloaded || i == nloaded - 1);
-	  unsigned int nmaps = i;
-
-	  /* 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, 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
-	     various members of this list cannot vanish since the open
-	     count is too high and will be decremented in this loop.  So
-	     we release the lock so that some code which might be called
-	     from a destructor can directly or indirectly access the
-	     lock.  */
-	  __rtld_lock_unlock_recursive (GL(dl_load_lock));
-
-	  /* 'maps' now contains the objects in the right order.  Now
-	     call the destructors.  We have to process this array from
-	     the front.  */
-	  for (i = 0; i < nmaps; ++i)
-	    {
-	      struct link_map *l = maps[i];
-
-	      if (l->l_init_called)
-		{
-		  _dl_call_fini (l);
 #ifdef SHARED
-		  /* Auditing checkpoint: another object closed.  */
-		  _dl_audit_objclose (l);
+	/* Auditing checkpoint: another object closed.  */
+	_dl_audit_objclose (l);
 #endif
-		}
-
-	      /* Correct the previous increment.  */
-	      --l->l_direct_opencount;
-	    }
+      }
 
 #ifdef SHARED
-	  _dl_audit_activity_nsid (ns, LA_ACT_CONSISTENT);
-#endif
-	}
-    }
-
-#ifdef SHARED
-  if (! do_audit && GLRO(dl_naudit) > 0)
-    {
-      do_audit = 1;
-      goto again;
-    }
+  if (last_ns >= 0)
+    _dl_audit_activity_nsid (last_ns, LA_ACT_CONSISTENT);
 
   if (__glibc_unlikely (GLRO(dl_debug_mask) & DL_DEBUG_STATISTICS))
     _dl_debug_printf ("\nruntime linker statistics:\n"
diff --git a/elf/dl-init.c b/elf/dl-init.c
index fca8e3a05e..77b2edd838 100644
--- a/elf/dl-init.c
+++ b/elf/dl-init.c
@@ -21,6 +21,7 @@
 #include <ldsodefs.h>
 #include <elf-initfini.h>
 
+struct link_map *_dl_init_called_list;
 
 static void
 call_init (struct link_map *l, int argc, char **argv, char **env)
@@ -42,6 +43,21 @@ call_init (struct link_map *l, int argc, char **argv, char **env)
      dependency.  */
   l->l_init_called = 1;
 
+  /* Help an already-running dlclose: The just-loaded object must not
+     be removed during the current pass.  (No effect if no dlclose in
+     progress.)  */
+  l->l_map_used = 1;
+
+  /* Record execution before starting any initializers.  This way, if
+     the initializers themselves call dlopen, their ELF destructors
+     will eventually be run before this object is destructed, matching
+     that their ELF constructors have run before this object was
+     constructed.  _dl_fini uses this list for audit callbacks, so
+     register objects on the list even if they do not have a
+     constructor.  */
+  l->l_init_called_next = _dl_init_called_list;
+  _dl_init_called_list = l;
+
   /* Check for object which constructors we do not run here.  */
   if (__builtin_expect (l->l_name[0], 'a') == '\0'
       && l->l_type == lt_executable)
diff --git a/elf/dso-sort-tests-1.def b/elf/dso-sort-tests-1.def
index 4bf9052db1..61dc54f8ae 100644
--- a/elf/dso-sort-tests-1.def
+++ b/elf/dso-sort-tests-1.def
@@ -53,21 +53,14 @@ tst-dso-ordering10: {}->a->b->c;soname({})=c
 output: b>a>{}<a<b
 
 # Complex example from Bugzilla #15311, under-linked and with circular
-# relocation(dynamic) dependencies. While this is technically unspecified, the
-# presumed reasonable practical behavior is for the destructor order to respect
-# the static DT_NEEDED links (here this means the a->b->c->d order).
-# The older dynamic_sort=1 algorithm does not achieve this, while the DFS-based
-# dynamic_sort=2 algorithm does, although it is still arguable whether going
-# beyond spec to do this is the right thing to do.
-# The below expected outputs are what the two algorithms currently produce
-# respectively, for regression testing purposes.
+# relocation(dynamic) dependencies. For both sorting algorithms, the
+# destruction order is the reverse of the construction order, and
+# relocation dependencies are not taken into account.
 tst-bz15311: {+a;+e;+f;+g;+d;%d;-d;-g;-f;-e;-a};a->b->c->d;d=>[ba];c=>a;b=>e=>a;c=>f=>b;d=>g=>c
-output(glibc.rtld.dynamic_sort=1): {+a[d>c>b>a>];+e[e>];+f[f>];+g[g>];+d[];%d(b(e(a()))a()g(c(a()f(b(e(a()))))));-d[];-g[];-f[];-e[];-a[<a<c<d<g<f<b<e];}
-output(glibc.rtld.dynamic_sort=2): {+a[d>c>b>a>];+e[e>];+f[f>];+g[g>];+d[];%d(b(e(a()))a()g(c(a()f(b(e(a()))))));-d[];-g[];-f[];-e[];-a[<g<f<a<b<c<d<e];}
+output: {+a[d>c>b>a>];+e[e>];+f[f>];+g[g>];+d[];%d(b(e(a()))a()g(c(a()f(b(e(a()))))));-d[];-g[];-f[];-e[];-a[<g<f<e<a<b<c<d];}
 
 # Test that even in the presence of dependency loops involving dlopen'ed
 # object, that object is initialized last (and not unloaded prematurely).
-# Final destructor order is indeterminate due to the cycle.
+# Final destructor order is the opposite of constructor order.
 tst-bz28937: {+a;+b;-b;+c;%c};a->a1;a->a2;a2->a;b->b1;c->a1;c=>a1
-output(glibc.rtld.dynamic_sort=1): {+a[a2>a1>a>];+b[b1>b>];-b[<b<b1];+c[c>];%c(a1());}<a<a2<c<a1
-output(glibc.rtld.dynamic_sort=2): {+a[a2>a1>a>];+b[b1>b>];-b[<b<b1];+c[c>];%c(a1());}<a2<a<c<a1
+output: {+a[a2>a1>a>];+b[b1>b>];-b[<b<b1];+c[c>];%c(a1());}<c<a<a1<a2
diff --git a/elf/tst-audit23.c b/elf/tst-audit23.c
index 4904cf1340..f40760bd70 100644
--- a/elf/tst-audit23.c
+++ b/elf/tst-audit23.c
@@ -98,6 +98,8 @@ do_test (int argc, char *argv[])
     char *lname;
     uintptr_t laddr;
     Lmid_t lmid;
+    uintptr_t cookie;
+    uintptr_t namespace;
     bool closed;
   } objs[max_objs] = { [0 ... max_objs-1] = { .closed = false } };
   size_t nobjs = 0;
@@ -117,6 +119,9 @@ do_test (int argc, char *argv[])
   size_t buffer_length = 0;
   while (xgetline (&buffer, &buffer_length, out))
     {
+      *strchrnul (buffer, '\n') = '\0';
+      printf ("info: subprocess output: %s\n", buffer);
+
       if (startswith (buffer, "la_activity: "))
 	{
 	  uintptr_t cookie;
@@ -125,29 +130,26 @@ do_test (int argc, char *argv[])
 			  &cookie);
 	  TEST_COMPARE (r, 2);
 
-	  /* The cookie identifies the object at the head of the link map,
-	     so we only add a new namespace if it changes from the previous
-	     one.  This works since dlmopen is the last in the test body.  */
-	  if (cookie != last_act_cookie && last_act_cookie != -1)
-	    TEST_COMPARE (last_act, LA_ACT_CONSISTENT);
-
 	  if (this_act == LA_ACT_ADD && acts[nacts] != cookie)
 	    {
+	      /* The cookie identifies the object at the head of the
+		 link map, so we only add a new namespace if it
+		 changes from the previous one.  This works since
+		 dlmopen is the last in the test body.  */
+	      if (cookie != last_act_cookie && last_act_cookie != -1)
+		TEST_COMPARE (last_act, LA_ACT_CONSISTENT);
+
 	      acts[nacts++] = cookie;
 	      last_act_cookie = cookie;
 	    }
-	  /* The LA_ACT_DELETE is called in the reverse order of LA_ACT_ADD
-	     at program termination (if the tests adds a dlclose or a library
-	     with extra dependencies this will need to be adapted).  */
+	  /* LA_ACT_DELETE is called multiple times for each
+	     namespace, depending on destruction order.  */
 	  else if (this_act == LA_ACT_DELETE)
-	    {
-	      last_act_cookie = acts[--nacts];
-	      TEST_COMPARE (acts[nacts], cookie);
-	      acts[nacts] = 0;
-	    }
+	    last_act_cookie = cookie;
 	  else if (this_act == LA_ACT_CONSISTENT)
 	    {
 	      TEST_COMPARE (cookie, last_act_cookie);
+	      last_act_cookie = -1;
 
 	      /* LA_ACT_DELETE must always be followed by an la_objclose.  */
 	      if (last_act == LA_ACT_DELETE)
@@ -179,6 +181,8 @@ do_test (int argc, char *argv[])
 	  objs[nobjs].lname = lname;
 	  objs[nobjs].laddr = laddr;
 	  objs[nobjs].lmid = lmid;
+	  objs[nobjs].cookie = cookie;
+	  objs[nobjs].namespace = last_act_cookie;
 	  objs[nobjs].closed = false;
 	  nobjs++;
 
@@ -201,6 +205,12 @@ do_test (int argc, char *argv[])
 	      if (strcmp (lname, objs[i].lname) == 0 && lmid == objs[i].lmid)
 		{
 		  TEST_COMPARE (objs[i].closed, false);
+		  TEST_COMPARE (objs[i].cookie, cookie);
+		  if (objs[i].namespace == -1)
+		    /* No LA_ACT_ADD before the first la_objopen call.  */
+		    TEST_COMPARE (acts[0], last_act_cookie);
+		  else
+		    TEST_COMPARE (objs[i].namespace, last_act_cookie);
 		  objs[i].closed = true;
 		  break;
 		}
@@ -209,11 +219,7 @@ do_test (int argc, char *argv[])
 	  /* la_objclose should be called after la_activity(LA_ACT_DELETE) for
 	     the closed object's namespace.  */
 	  TEST_COMPARE (last_act, LA_ACT_DELETE);
-	  if (!seen_first_objclose)
-	    {
-	      TEST_COMPARE (last_act_cookie, cookie);
-	      seen_first_objclose = true;
-	    }
+	  seen_first_objclose = true;
 	}
     }
 
diff --git a/include/link.h b/include/link.h
index 0ac82d7c77..87966e8397 100644
--- a/include/link.h
+++ b/include/link.h
@@ -278,6 +278,10 @@ struct link_map
     /* List of object in order of the init and fini calls.  */
     struct link_map **l_initfini;
 
+    /* Linked list of objects in reverse ELF constructor execution
+       order.  Head of list is stored in _dl_init_called_list.  */
+    struct link_map *l_init_called_next;
+
     /* List of the dependencies introduced through symbol binding.  */
     struct link_map_reldeps
       {
diff --git a/sysdeps/generic/ldsodefs.h b/sysdeps/generic/ldsodefs.h
index c2627fced7..ab8a7fbf84 100644
--- a/sysdeps/generic/ldsodefs.h
+++ b/sysdeps/generic/ldsodefs.h
@@ -1047,6 +1047,10 @@ extern int _dl_check_map_versions (struct link_map *map, int verbose,
 extern void _dl_init (struct link_map *main_map, int argc, char **argv,
 		      char **env) attribute_hidden;
 
+/* List of ELF objects in reverse order of their constructor
+   invocation.  */
+extern struct link_map *_dl_init_called_list attribute_hidden;
+
 /* Call the finalizer functions of all shared objects whose
    initializer functions have completed.  */
 extern void _dl_fini (void) attribute_hidden;