diff --git a/elf/Makefile b/elf/Makefile
index 5e809dbfaa..834ec858a8 100644
--- a/elf/Makefile
+++ b/elf/Makefile
@@ -334,7 +334,7 @@ modules-names = testobj1 testobj2 testobj3 testobj4 testobj5 testobj6 \
 		tst-auditmanymod7 tst-auditmanymod8 tst-auditmanymod9 \
 		tst-initlazyfailmod tst-finilazyfailmod \
 		tst-dlopenfailmod1 tst-dlopenfaillinkmod tst-dlopenfailmod2 \
-		tst-dlopenfailmod3 tst-ldconfig-ld-mod \
+		tst-dlopenfailmod3 tst-dlopenfailnodelmod tst-ldconfig-ld-mod \
 		tst-filterobj-flt tst-filterobj-aux tst-filterobj-filtee \
 		tst-auditlogmod-1 tst-auditlogmod-2 tst-auditlogmod-3 \
 		tst-single_threaded-mod1 tst-single_threaded-mod2 \
@@ -1733,11 +1733,18 @@ LDFLAGS-tst-dlopenfailmod1.so = -Wl,--no-as-needed
 $(objpfx)tst-dlopenfailmod1.so: \
   $(shared-thread-library) $(objpfx)tst-dlopenfaillinkmod.so
 LDFLAGS-tst-dlopenfaillinkmod.so = -Wl,-soname,tst-dlopenfail-missingmod.so
-$(objpfx)tst-dlopenfailmod2.so: $(shared-thread-library)
+$(objpfx)tst-dlopenfailmod2.so: $(objpfx)tst-dlopenfailnodelmod.so
 $(objpfx)tst-dlopenfail-2: $(libdl)
 $(objpfx)tst-dlopenfail-2.out: \
   $(objpfx)tst-dlopenfailmod1.so $(objpfx)tst-dlopenfailmod2.so \
   $(objpfx)tst-dlopenfailmod3.so
+# tst-dlopenfailnodelmod.so emulates how libpthread was linked.
+$(objpfx)tst-dlopenfailnodelmod.so: $(libsupport)
+LDFLAGS-tst-dlopenfailnodelmod.so = \
+  -Wl,--enable-new-dtags,-z,nodelete,-z,initfirst
+# tst-dlopenfail should export the libsupport symbols, so that
+# tst-dlopenfailnodelmod.so uses them for error reporting.
+LDFLAGS-tst-dlopenfail = -Wl,-E
 
 $(objpfx)tst-dlopen-nodelete-reloc: $(libdl)
 $(objpfx)tst-dlopen-nodelete-reloc.out: \
diff --git a/elf/tst-dlopenfail-2.c b/elf/tst-dlopenfail-2.c
index 50eed81cb0..168c4b2c7f 100644
--- a/elf/tst-dlopenfail-2.c
+++ b/elf/tst-dlopenfail-2.c
@@ -28,10 +28,7 @@
 static int
 do_test (void)
 {
-  /* This test uses libpthread as the canonical NODELETE module.  If
-     libpthread is no longer NODELETE because it has been merged into
-     libc, the test needs to be updated.  */
-  TEST_VERIFY (dlsym (NULL, "pthread_create") == NULL);
+  TEST_VERIFY (dlsym (NULL, "no_delete_mod_function") == NULL);
 
   /* This is expected to fail because of the missing dependency.  */
   puts ("info: attempting to load tst-dlopenfailmod1.so");
diff --git a/elf/tst-dlopenfail.c b/elf/tst-dlopenfail.c
index db2b41f9b5..990e28dbce 100644
--- a/elf/tst-dlopenfail.c
+++ b/elf/tst-dlopenfail.c
@@ -18,7 +18,6 @@
 
 #include <dlfcn.h>
 #include <errno.h>
-#include <gnu/lib-names.h>
 #include <stddef.h>
 #include <stdio.h>
 #include <string.h>
@@ -28,10 +27,7 @@
 static int
 do_test (void)
 {
-  /* This test uses libpthread as the canonical NODELETE module.  If
-     libpthread is no longer NODELETE because it has been merged into
-     libc, the test needs to be updated.  */
-  TEST_VERIFY (dlsym (NULL, "pthread_create") == NULL);
+  TEST_VERIFY (dlsym (NULL, "no_delete_mod_function") == NULL);
 
   /* This is expected to fail because of the missing dependency.  */
   puts ("info: attempting to load tst-dlopenfailmod1.so");
@@ -42,36 +38,30 @@ do_test (void)
                        " cannot open shared object file:"
                        " No such file or directory");
 
-  /* Do not probe for the presence of libpthread at this point because
-     that might trigger relocation if bug 20839 is present, obscuring
-     a subsequent crash.  */
+  /* Do not probe for the presence of the tst-dlopenfailnodelmod.so at
+     this point because that might trigger relocation if bug 20839 is
+     present, obscuring a subsequent crash.  */
 
   /* This is expected to succeed.  */
   puts ("info: loading tst-dlopenfailmod2.so");
   void *handle = xdlopen ("tst-dlopenfailmod2.so", RTLD_NOW);
+  xdlsym (handle, "no_delete_mod_function");
   xdlclose (handle);
 
-  /* libpthread should remain loaded.  */
-  TEST_VERIFY (dlopen (LIBPTHREAD_SO, RTLD_LAZY | RTLD_NOLOAD) != NULL);
-  TEST_VERIFY (dlsym (NULL, "pthread_create") == NULL);
+  /* The NODELETE module should remain loaded.  */
+  xdlopen ("tst-dlopenfailnodelmod.so", RTLD_LAZY | RTLD_NOLOAD);
+  /* But the symbol is not in the global scope.  */
+  TEST_VERIFY (dlsym (NULL, "no_delete_mod_function") == NULL);
 
-  /* We can make libpthread global, and then the symbol should become
-     available.  */
-  TEST_VERIFY (dlopen (LIBPTHREAD_SO, RTLD_LAZY | RTLD_GLOBAL) != NULL);
-  TEST_VERIFY (dlsym (NULL, "pthread_create") != NULL);
+  /* We can make tst-dlopenfailnodelmod.so global, and then the symbol
+     should become available.  */
+  xdlopen ("tst-dlopenfailnodelmod.so", RTLD_LAZY | RTLD_GLOBAL);
+  void (*no_delete_mod_function) (void)
+    = xdlsym (NULL, "no_delete_mod_function");
 
-  /* sem_open is sufficiently complex to depend on relocations.  */
-  void *(*sem_open_ptr) (const char *, int flag, ...)
-    = dlsym (NULL, "sem_open");
-  if (sem_open_ptr == NULL)
-    /* Hurd does not implement sem_open.  */
-    puts ("warning: sem_open not found, further testing not possible");
-  else
-    {
-      errno = 0;
-      TEST_VERIFY (sem_open_ptr ("/", 0) == NULL);
-      TEST_COMPARE (errno, EINVAL);
-    }
+  /* Hopefully, no_delete_mod_function is sufficiently complex to
+     depend on relocations.  */
+  no_delete_mod_function ();
 
   return 0;
 }
diff --git a/elf/tst-dlopenfailmod2.c b/elf/tst-dlopenfailmod2.c
index cd6f9cf56b..ed353f9a3c 100644
--- a/elf/tst-dlopenfailmod2.c
+++ b/elf/tst-dlopenfailmod2.c
@@ -16,11 +16,11 @@
    License along with the GNU C Library; if not, see
    <https://www.gnu.org/licenses/>.  */
 
-#include <pthread.h>
 #include <stdio.h>
 
-/* Force linking against libpthread.  */
-void *pthread_create_reference = pthread_create;
+/* Force linking against tst-dlopenfailnodelmod.so.  */
+void no_delete_mod_function (void);
+void *function_reference = no_delete_mod_function;
 
 static void __attribute__ ((constructor))
 init (void)
diff --git a/elf/tst-dlopenfailnodelmod.c b/elf/tst-dlopenfailnodelmod.c
new file mode 100644
index 0000000000..c4347b7591
--- /dev/null
+++ b/elf/tst-dlopenfailnodelmod.c
@@ -0,0 +1,29 @@
+/* NODELETE module for tst-dlopenfail, tst-dlopenfail-2.
+   Copyright (C) 2021 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include <support/check.h>
+
+/* Introduce some relocation dependencies.  */
+const char test_string[] = "test string";
+const char *test_string_ptr = test_string;
+
+void
+no_delete_mod_function (void)
+{
+  TEST_COMPARE_STRING (test_string, test_string_ptr);
+}
