diff --git a/misc/tsearch.c b/misc/tsearch.c
index 9b2eb34b25..e517dfa712 100644
--- a/misc/tsearch.c
+++ b/misc/tsearch.c
@@ -85,6 +85,7 @@
 #include <assert.h>
 #include <stdalign.h>
 #include <stddef.h>
+#include <stdint.h>
 #include <stdlib.h>
 #include <string.h>
 #include <search.h>
@@ -406,12 +407,13 @@ __tdelete (const void *key, void **vrootp, __compar_fn_t compar)
   int cmp;
   node *rootp = (node *) vrootp;
   node root, unchained;
-  /* Stack of nodes so we remember the parents without recursion.  It's
-     _very_ unlikely that there are paths longer than 40 nodes.  The tree
-     would need to have around 250.000 nodes.  */
-  int stacksize = 40;
+  /* Stack of nodes so we remember the parents without recursion.  The
+     stack size is a conservative approximation of the maximum height
+     of a red-black tree, based on size of the address space.
+     Actual numbers are closer to 57 (32 bit) and 117 (63 bit).  */
+  enum { stacksize = 2 * UINTPTR_WIDTH };
   int sp = 0;
-  node **nodestack = alloca (sizeof (node *) * stacksize);
+  node *nodestack[stacksize];
 
   if (rootp == NULL)
     return NULL;
@@ -424,14 +426,7 @@ __tdelete (const void *key, void **vrootp, __compar_fn_t compar)
   root = DEREFNODEPTR(rootp);
   while ((cmp = (*compar) (key, root->key)) != 0)
     {
-      if (sp == stacksize)
-	{
-	  node **newstack;
-	  stacksize += 20;
-	  newstack = alloca (sizeof (node *) * stacksize);
-	  nodestack = memcpy (newstack, nodestack, sp * sizeof (node *));
-	}
-
+      assert (sp < stacksize);
       nodestack[sp++] = rootp;
       p = DEREFNODEPTR(rootp);
       if (cmp < 0)
@@ -470,13 +465,7 @@ __tdelete (const void *key, void **vrootp, __compar_fn_t compar)
       node upn;
       for (;;)
 	{
-	  if (sp == stacksize)
-	    {
-	      node **newstack;
-	      stacksize += 20;
-	      newstack = alloca (sizeof (node *) * stacksize);
-	      nodestack = memcpy (newstack, nodestack, sp * sizeof (node *));
-	    }
+	  assert (sp < stacksize);
 	  nodestack[sp++] = parentp;
 	  parentp = up;
 	  upn = DEREFNODEPTR(up);
@@ -541,6 +530,7 @@ __tdelete (const void *key, void **vrootp, __compar_fn_t compar)
 		  SETNODEPTR(pp,q);
 		  /* Make sure pp is right if the case below tries to use
 		     it.  */
+		  assert (sp < stacksize);
 		  nodestack[sp++] = pp = LEFTPTR(q);
 		  q = RIGHT(p);
 		}
@@ -625,6 +615,7 @@ __tdelete (const void *key, void **vrootp, __compar_fn_t compar)
 		  SETLEFT(p,RIGHT(q));
 		  SETRIGHT(q,p);
 		  SETNODEPTR(pp,q);
+		  assert (sp < stacksize);
 		  nodestack[sp++] = pp = RIGHTPTR(q);
 		  q = LEFT(p);
 		}