diff --git a/nptl/Makefile b/nptl/Makefile
index 5f85dd7854..33766eaf7a 100644
--- a/nptl/Makefile
+++ b/nptl/Makefile
@@ -386,10 +386,6 @@ xtests += tst-eintr1
 
 test-srcs = tst-oddstacklimit
 
-# Test expected to fail on most targets (except x86_64) due to bug
-# 18435 - pthread_once hangs when init routine throws an exception.
-test-xfail-tst-once5 = yes
-
 gen-as-const-headers = unwindbuf.sym \
 		       pthread-pi-defines.sym
 
diff --git a/nptl/pthreadP.h b/nptl/pthreadP.h
index d2fd0826fe..93f3cef00f 100644
--- a/nptl/pthreadP.h
+++ b/nptl/pthreadP.h
@@ -604,6 +604,67 @@ extern void __pthread_cleanup_pop (struct _pthread_cleanup_buffer *buffer,
 # undef pthread_cleanup_pop
 # define pthread_cleanup_pop(execute)                   \
   __pthread_cleanup_pop (&_buffer, (execute)); }
+
+# if defined __EXCEPTIONS && !defined __cplusplus
+/* Structure to hold the cleanup handler information.  */
+struct __pthread_cleanup_combined_frame
+{
+  void (*__cancel_routine) (void *);
+  void *__cancel_arg;
+  int __do_it;
+  struct _pthread_cleanup_buffer __buffer;
+};
+
+/* Special cleanup macros which register cleanup both using
+   __pthread_cleanup_{push,pop} and using cleanup attribute.  This is needed
+   for pthread_once, so that it supports both throwing exceptions from the
+   pthread_once callback (only cleanup attribute works there) and cancellation
+   of the thread running the callback if the callback or some routines it
+   calls don't have unwind information.  */
+
+static __always_inline void
+__pthread_cleanup_combined_routine (struct __pthread_cleanup_combined_frame
+				    *__frame)
+{
+  if (__frame->__do_it)
+    {
+      __frame->__cancel_routine (__frame->__cancel_arg);
+      __frame->__do_it = 0;
+      __pthread_cleanup_pop (&__frame->__buffer, 0);
+    }
+}
+
+static inline void
+__pthread_cleanup_combined_routine_voidptr (void *__arg)
+{
+  struct __pthread_cleanup_combined_frame *__frame
+    = (struct __pthread_cleanup_combined_frame *) __arg;
+  if (__frame->__do_it)
+    {
+      __frame->__cancel_routine (__frame->__cancel_arg);
+      __frame->__do_it = 0;
+    }
+}
+
+#  define pthread_cleanup_combined_push(routine, arg) \
+  do {									      \
+    void (*__cancel_routine) (void *) = (routine);			      \
+    struct __pthread_cleanup_combined_frame __clframe			      \
+      __attribute__ ((__cleanup__ (__pthread_cleanup_combined_routine)))      \
+      = { .__cancel_routine = __cancel_routine, .__cancel_arg = (arg),	      \
+	  .__do_it = 1 };						      \
+    __pthread_cleanup_push (&__clframe.__buffer,			      \
+			    __pthread_cleanup_combined_routine_voidptr,	      \
+			    &__clframe);
+
+#  define pthread_cleanup_combined_pop(execute) \
+    __pthread_cleanup_pop (&__clframe.__buffer, 0);			      \
+    __clframe.__do_it = 0;						      \
+    if (execute)							      \
+      __cancel_routine (__clframe.__cancel_arg);			      \
+  } while (0)
+
+# endif
 #endif
 
 extern void __pthread_cleanup_push_defer (struct _pthread_cleanup_buffer *buffer,
diff --git a/nptl/pthread_once.c b/nptl/pthread_once.c
index 28d97097c7..7645da222a 100644
--- a/nptl/pthread_once.c
+++ b/nptl/pthread_once.c
@@ -111,11 +111,11 @@ __pthread_once_slow (pthread_once_t *once_control, void (*init_routine) (void))
       /* This thread is the first here.  Do the initialization.
 	 Register a cleanup handler so that in case the thread gets
 	 interrupted the initialization can be restarted.  */
-      pthread_cleanup_push (clear_once_control, once_control);
+      pthread_cleanup_combined_push (clear_once_control, once_control);
 
       init_routine ();
 
-      pthread_cleanup_pop (0);
+      pthread_cleanup_combined_pop (0);
 
 
       /* Mark *once_control as having finished the initialization.  We need
diff --git a/nptl/tst-once5.cc b/nptl/tst-once5.cc
index b797ab3562..60fe1ef820 100644
--- a/nptl/tst-once5.cc
+++ b/nptl/tst-once5.cc
@@ -59,7 +59,7 @@ do_test (void)
                " throwing an exception", stderr);
     }
     catch (OnceException) {
-      if (1 < niter)
+      if (niter > 1)
         fputs ("pthread_once unexpectedly threw", stderr);
       result = 0;
     }
@@ -75,7 +75,5 @@ do_test (void)
   return result;
 }
 
-// The test currently hangs and is XFAILed.  Reduce the timeout.
-#define TIMEOUT 1
 #define TEST_FUNCTION do_test ()
 #include "../test-skeleton.c"
diff --git a/sysdeps/pthread/Makefile b/sysdeps/pthread/Makefile
index eeb64f9fb0..53b65ef349 100644
--- a/sysdeps/pthread/Makefile
+++ b/sysdeps/pthread/Makefile
@@ -231,7 +231,7 @@ generated += $(objpfx)tst-atfork2.mtrace \
 
 tests-internal += tst-cancel25 tst-robust8
 
-tests += tst-oncex3 tst-oncex4
+tests += tst-oncex3 tst-oncex4 tst-oncey3 tst-oncey4
 
 modules-names += tst-join7mod
 
@@ -242,6 +242,8 @@ endif
 
 CFLAGS-tst-oncex3.c += -fexceptions
 CFLAGS-tst-oncex4.c += -fexceptions
+CFLAGS-tst-oncey3.c += -fno-exceptions -fno-asynchronous-unwind-tables
+CFLAGS-tst-oncey4.c += -fno-exceptions -fno-asynchronous-unwind-tables
 
 $(objpfx)tst-join7: $(libdl) $(shared-thread-library)
 $(objpfx)tst-join7.out: $(objpfx)tst-join7mod.so
diff --git a/sysdeps/pthread/tst-oncey3.c b/sysdeps/pthread/tst-oncey3.c
new file mode 100644
index 0000000000..08225b88dc
--- /dev/null
+++ b/sysdeps/pthread/tst-oncey3.c
@@ -0,0 +1 @@
+#include "tst-once3.c"
diff --git a/sysdeps/pthread/tst-oncey4.c b/sysdeps/pthread/tst-oncey4.c
new file mode 100644
index 0000000000..9b4d98f3f1
--- /dev/null
+++ b/sysdeps/pthread/tst-oncey4.c
@@ -0,0 +1 @@
+#include "tst-once4.c"