diff --git a/mysql-test/t/multi_update2.test b/mysql-test/t/multi_update2.test
index 47f9bc7bad7..9341d40282b 100644
--- a/mysql-test/t/multi_update2.test
+++ b/mysql-test/t/multi_update2.test
@@ -2,14 +2,27 @@
 # Test of update statement that uses many tables.
 #
 
+#
+# If we are running with
+# - Valgrind           -> $VALGRIND_TEST <> 0
+# - debug tracing      -> @@debug LIKE '%trace%'
+# the resource consumtion (storage space needed, runtime) will be extreme.
+# Therefore we require that option "big" is set.
+#
+
+if (`SELECT ($VALGRIND_TEST <> 0 OR @@debug LIKE '%trace%') AND '$BIG_TEST' = ''`)
+{
+  --skip Need "big" when running with Valgrind or debug
+}
+
+#
+# Bug#1820 Rows not deleted from second table on multi-table delete
+#
+
 --disable_warnings
 DROP TABLE IF EXISTS t1,t2;
 --enable_warnings
 
-#
-# Bug#1820 Rows not deleted from second table on multi-table delete
-#
-
 CREATE TABLE t1 ( a INT NOT NULL, b INT NOT NULL) ;
 --echo # The protocolling of many inserts into t1 is suppressed.
 --disable_query_log