diff --git a/mysql-test/main/show_explain.test b/mysql-test/main/show_explain.test
index 515eb9efa47..415a892c0ec 100644
--- a/mysql-test/main/show_explain.test
+++ b/mysql-test/main/show_explain.test
@@ -3,7 +3,8 @@
 #
 --source include/have_debug.inc
 --source include/have_innodb.inc
-
+# Using valgrind can cause 'reap' to fail. See comment below
+--source include/not_valgrind.inc
 
 --disable_warnings
 drop table if exists t0, t1, t2, t3, t4;
@@ -885,6 +886,7 @@ let $wait_condition= select State='show explain' from information_schema.process
 evalp kill query $thr_default;
 
 connection default;
+# This may fail when using valgrind
 --error ER_QUERY_INTERRUPTED
 reap;
 
diff --git a/mysql-test/main/ssl-big.test b/mysql-test/main/ssl-big.test
index 367cbcba2d7..44db11b52bb 100644
--- a/mysql-test/main/ssl-big.test
+++ b/mysql-test/main/ssl-big.test
@@ -4,6 +4,8 @@
 -- source include/have_ssl_communication.inc
 -- source include/big_test.inc
 -- source include/have_64bit.inc
+# No point in running with valgrind as it takes 1.5 hours
+-- source include/not_valgrind.inc
 
 # Save the initial number of concurrent sessions
 --source include/count_sessions.inc