diff --git a/elf/Makefile b/elf/Makefile
index dea51ca182..5e4cdb494f 100644
--- a/elf/Makefile
+++ b/elf/Makefile
@@ -192,14 +192,16 @@ tests += restest1 preloadtest loadfail multiload origtest resolvfail \
 	 tst-latepthread tst-tls-manydynamic tst-nodelete-dlclose \
 	 tst-debug1 tst-main1 tst-absolute-sym tst-absolute-zero tst-big-note \
 	 tst-unwind-ctor tst-unwind-main tst-audit13 \
-	 tst-sonamemove-link tst-sonamemove-dlopen tst-dlopen-aout
+	 tst-sonamemove-link tst-sonamemove-dlopen tst-dlopen-tlsmodid \
+	 tst-dlopen-self
 #	 reldep9
 tests-internal += loadtest unload unload2 circleload1 \
 	 neededtest neededtest2 neededtest3 neededtest4 \
 	 tst-tls3 tst-tls6 tst-tls7 tst-tls8 tst-dlmopen2 \
 	 tst-ptrguard1 tst-stackguard1 tst-libc_dlvsym \
 	 tst-create_format1
-tests-container += tst-pldd tst-dlopen-aout-container
+tests-container += tst-pldd tst-dlopen-tlsmodid-container \
+  tst-dlopen-self-container
 test-srcs = tst-pathopt
 selinux-enabled := $(shell cat /selinux/enforce 2> /dev/null)
 ifneq ($(selinux-enabled),1)
@@ -308,8 +310,9 @@ test-xfail-tst-protected1b = yes
 endif
 ifeq (yesyes,$(have-fpie)$(build-shared))
 modules-names += tst-piemod1
-tests += tst-pie1 tst-pie2 tst-dlopen-pie tst-dlopen-aout-pie
-tests-pie += tst-pie1 tst-pie2 tst-dlopen-aout-pie
+tests += tst-pie1 tst-pie2 tst-dlopen-pie tst-dlopen-tlsmodid-pie \
+  tst-dlopen-self-pie
+tests-pie += tst-pie1 tst-pie2 tst-dlopen-tlsmodid-pie tst-dlopen-self-pie
 ifeq (yes,$(have-protected-data))
 tests += vismain
 tests-pie += vismain
@@ -1268,12 +1271,21 @@ $(objpfx)tst-addr1: $(libdl)
 
 $(objpfx)tst-thrlock: $(libdl) $(shared-thread-library)
 
-tst-tst-dlopen-aout-no-pie = yes
-$(objpfx)tst-dlopen-aout: $(libdl) $(shared-thread-library)
-CFLAGS-tst-dlopen-aout-pie.c += $(pie-ccflag)
-$(objpfx)tst-dlopen-aout-pie: $(libdl) $(shared-thread-library)
-$(objpfx)tst-dlopen-aout-container: $(libdl) $(shared-thread-library)
-LDFLAGS-tst-dlopen-aout-container += -Wl,-rpath,\$$ORIGIN
+tst-tst-dlopen-tlsmodid-no-pie = yes
+$(objpfx)tst-dlopen-tlsmodid: $(libdl) $(shared-thread-library)
+$(objpfx)tst-dlopen-tlsmodid.out: $(objpfx)tst-dlopen-self
+CFLAGS-tst-dlopen-tlsmodid-pie.c += $(pie-ccflag)
+$(objpfx)tst-dlopen-tlsmodid-pie: $(libdl) $(shared-thread-library)
+$(objpfx)tst-dlopen-tlsmodid-pie.out: $(objpfx)tst-dlopen-self-pie
+$(objpfx)tst-dlopen-tlsmodid-container: $(libdl) $(shared-thread-library)
+LDFLAGS-tst-dlopen-tlsmodid-container += -Wl,-rpath,\$$ORIGIN
+
+tst-tst-dlopen-self-no-pie = yes
+$(objpfx)tst-dlopen-self: $(libdl)
+CFLAGS-tst-dlopen-self-pie.c += $(pie-ccflag)
+$(objpfx)tst-dlopen-self-pie: $(libdl)
+$(objpfx)tst-dlopen-self-container: $(libdl)
+LDFLAGS-tst-dlopen-self-container += -Wl,-rpath,\$$ORIGIN
 
 CFLAGS-ifuncmain1pic.c += $(pic-ccflag)
 CFLAGS-ifuncmain1picstatic.c += $(pic-ccflag)
diff --git a/elf/tst-dlopen-self-container.c b/elf/tst-dlopen-self-container.c
new file mode 100644
index 0000000000..b1db238dec
--- /dev/null
+++ b/elf/tst-dlopen-self-container.c
@@ -0,0 +1,19 @@
+/* Check dlopen'ing the executable itself fails (bug 24900); container version.
+   Copyright (C) 2014-2019 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 "tst-dlopen-self.c"
diff --git a/elf/tst-dlopen-aout-container.c b/elf/tst-dlopen-self-pie.c
similarity index 87%
rename from elf/tst-dlopen-aout-container.c
rename to elf/tst-dlopen-self-pie.c
index 702dbe04c4..855bccc5b5 100644
--- a/elf/tst-dlopen-aout-container.c
+++ b/elf/tst-dlopen-self-pie.c
@@ -1,4 +1,4 @@
-/* Test case for BZ #16634 and BZ#24900.  Container version.
+/* Check that dlopen'ing the executable itself fails (bug 24900); PIE version.
    Copyright (C) 2014-2019 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
 
@@ -16,4 +16,4 @@
    License along with the GNU C Library; if not, see
    <https://www.gnu.org/licenses/>.  */
 
-#include "tst-dlopen-aout.c"
+#include "tst-dlopen-self.c"
diff --git a/elf/tst-dlopen-self.c b/elf/tst-dlopen-self.c
new file mode 100644
index 0000000000..310f1b09d4
--- /dev/null
+++ b/elf/tst-dlopen-self.c
@@ -0,0 +1,55 @@
+/* Check that dlopen'ing the executable itself fails (bug 24900).
+   Copyright (C) 2014-2019 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 <dlfcn.h>
+#include <stdlib.h>
+#include <string.h>
+#include <support/check.h>
+
+/* Call dlopen and check that fails with an error message indicating
+   an attempt to open an ET_EXEC or PIE object.  */
+static void
+check_dlopen_failure (const char *path)
+{
+  void *handle = dlopen (path, RTLD_LAZY);
+  if (handle != NULL)
+    FAIL_EXIT1 ("dlopen succeeded unexpectedly: %s", path);
+
+  const char *message = dlerror ();
+  TEST_VERIFY_EXIT (message != NULL);
+  if ((strstr (message,
+	       "cannot dynamically load position-independent executable")
+       == NULL)
+      && strstr (message, "cannot dynamically load executable") == NULL)
+    FAIL_EXIT1 ("invalid dlopen error message: \"%s\"", message);
+}
+
+static int
+do_test (int argc, char *argv[])
+{
+  check_dlopen_failure (argv[0]);
+
+  char *full_path = realpath (argv[0], NULL);
+  check_dlopen_failure  (full_path);
+  free (full_path);
+
+  return 0;
+}
+
+#define TEST_FUNCTION_ARGV do_test
+#include <support/test-driver.c>
diff --git a/elf/tst-dlopen-tlsmodid-container.c b/elf/tst-dlopen-tlsmodid-container.c
new file mode 100644
index 0000000000..7654fcb214
--- /dev/null
+++ b/elf/tst-dlopen-tlsmodid-container.c
@@ -0,0 +1,39 @@
+/* Test case for BZ #16634.  Container version.
+   Copyright (C) 2014-2019 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/>.  */
+
+/* This test use the iconv program as the test binary.  */
+
+#include <stdlib.h>
+#include <support/support.h>
+
+static char *iconv_path;
+
+static __attribute__ ((constructor)) void
+iconv_path_init (void)
+{
+  iconv_path = xasprintf ("%s/iconv", support_bindir_prefix);
+}
+
+static __attribute__ ((destructor)) void
+iconv_path_fini (void)
+{
+  free (iconv_path);
+}
+
+#define TST_DLOPEN_TLSMODID_PATH iconv_path
+#include "tst-dlopen-tlsmodid.h"
diff --git a/elf/tst-dlopen-aout-pie.c b/elf/tst-dlopen-tlsmodid-pie.c
similarity index 85%
rename from elf/tst-dlopen-aout-pie.c
rename to elf/tst-dlopen-tlsmodid-pie.c
index 8d2009c0f3..db1176b12c 100644
--- a/elf/tst-dlopen-aout-pie.c
+++ b/elf/tst-dlopen-tlsmodid-pie.c
@@ -1,4 +1,4 @@
-/* Test case for BZ #16634 and BZ#24900.  PIE version.
+/* Test case for BZ #16634.  PIE version.
    Copyright (C) 2014-2019 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
 
@@ -16,4 +16,5 @@
    License along with the GNU C Library; if not, see
    <http://www.gnu.org/licenses/>.  */
 
-#include "tst-dlopen-aout.c"
+#define TST_DLOPEN_TLSMODID_PATH "tst-dlopen-self-pie"
+#include "tst-dlopen-tlsmodid.h"
diff --git a/elf/tst-dlopen-tlsmodid.c b/elf/tst-dlopen-tlsmodid.c
new file mode 100644
index 0000000000..165edcb552
--- /dev/null
+++ b/elf/tst-dlopen-tlsmodid.c
@@ -0,0 +1,25 @@
+/* Test case for BZ #16634.  Non-PIE version.
+
+   Verify that incorrectly dlopen()ing an executable without
+   __RTLD_OPENEXEC does not cause assertion in ld.so, and that it
+   actually results in an error.
+
+   Copyright (C) 2014-2019 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/>.  */
+
+#define TST_DLOPEN_TLSMODID_PATH "tst-dlopen-self"
+#include "tst-dlopen-tlsmodid.h"
diff --git a/elf/tst-dlopen-aout.c b/elf/tst-dlopen-tlsmodid.h
similarity index 77%
rename from elf/tst-dlopen-aout.c
rename to elf/tst-dlopen-tlsmodid.h
index b86d082bc1..c747cb1491 100644
--- a/elf/tst-dlopen-aout.c
+++ b/elf/tst-dlopen-tlsmodid.h
@@ -1,4 +1,5 @@
-/* Test case for BZ #16634 and BZ#24900.
+/* Common code for tst-dlopen-tlsmodid, tst-dlopen-tlsmodid-pie,
+   tst-dlopen-tlsmodid-container.
 
    Verify that incorrectly dlopen()ing an executable without
    __RTLD_OPENEXEC does not cause assertion in ld.so, and that it
@@ -21,6 +22,9 @@
    License along with the GNU C Library; if not, see
    <https://www.gnu.org/licenses/>.  */
 
+/* Before including this file, the macro TST_DLOPEN_TLSMODID_PATH must
+   be defined, to specify the path used for the open operation.  */
+
 #include <dlfcn.h>
 #include <pthread.h>
 #include <stdio.h>
@@ -38,14 +42,14 @@ fn (void *p)
   return p;
 }
 
-/* Call dlopen on PATH and check that fails with an error message
-   indicating an attempt to open an ET_EXEC or PIE object.  */
+/* Call dlopen and check that fails with an error message indicating
+   an attempt to open an ET_EXEC or PIE object.  */
 static void
-check_dlopen_failure (const char *path)
+check_dlopen_failure (void)
 {
-  void *handle = dlopen (path, RTLD_LAZY);
+  void *handle = dlopen (TST_DLOPEN_TLSMODID_PATH, RTLD_LAZY);
   if (handle != NULL)
-    FAIL_EXIT1 ("dlopen succeeded unexpectedly: %s", path);
+    FAIL_EXIT1 ("dlopen succeeded unexpectedly: %s", TST_DLOPEN_TLSMODID_PATH);
 
   const char *message = dlerror ();
   TEST_VERIFY_EXIT (message != NULL);
@@ -65,7 +69,7 @@ do_test (int argc, char *argv[])
     {
       pthread_t thr;
 
-      check_dlopen_failure (argv[0]);
+      check_dlopen_failure ();
 
       /* We create threads to force TLS allocation, which triggers
 	 the original bug i.e. running out of surplus slotinfo entries
@@ -74,9 +78,7 @@ do_test (int argc, char *argv[])
       xpthread_join (thr);
     }
 
-  /* The elf subdirectory (or $ORIGIN in the container case) is on the
-     library search path.  */
-  check_dlopen_failure ("tst-dlopen-aout");
+  check_dlopen_failure ();
 
   return 0;
 }
