diff --git a/mysql-test/extra/rpl_tests/rpl_insert_id.test b/mysql-test/extra/rpl_tests/rpl_insert_id.test
index 8ee98e0bc76..0cc0a343304 100644
--- a/mysql-test/extra/rpl_tests/rpl_insert_id.test
+++ b/mysql-test/extra/rpl_tests/rpl_insert_id.test
@@ -18,6 +18,13 @@ use test;
 drop table if exists t1, t2, t3;
 --enable_warnings
 
+# If concurrent inserts are on, it is not guaranteed that the rows
+# inserted by INSERT are immediately accessible by SELECT in another
+# thread. This would cause problems near the line 'connection master1'
+# below. So we turn off concurrent inserts.
+SET @old_concurrent_insert= @@global.concurrent_insert;
+SET @@global.concurrent_insert= 0;
+
 --echo #
 --echo # See if queries that use both auto_increment and LAST_INSERT_ID()
 --echo # are replicated well
@@ -29,8 +36,8 @@ drop table if exists t1, t2, t3;
 #should work for both SBR and RBR
 
 connection master;
-create table t1(a int auto_increment, key(a));
-create table t2(b int auto_increment, c int, key(b));
+eval create table t1(a int auto_increment, key(a)) engine=$engine_type;
+eval create table t2(b int auto_increment, c int, key(b)) engine=$engine_type;
 insert into t1 values (1),(2),(3);
 insert into t1 values (null);
 insert into t2 values (null,last_insert_id());
@@ -68,8 +75,8 @@ connection master;
 
 drop table t2;
 drop table t1;
-create table t1(a int auto_increment, key(a));
-create table t2(b int auto_increment, c int, key(b));
+eval create table t1(a int auto_increment, key(a)) engine=$engine_type;
+eval create table t2(b int auto_increment, c int, key(b)) engine=$engine_type;
 insert into t1 values (10);
 insert into t1 values (null),(null),(null);
 insert into t2 values (5,0);
@@ -94,7 +101,7 @@ sync_with_master;
 
 connection master;
 SET TIMESTAMP=1000000000;
-CREATE TABLE t1 ( a INT UNIQUE );
+eval CREATE TABLE t1 ( a INT UNIQUE ) engine=$engine_type;
 SET FOREIGN_KEY_CHECKS=0;
 # Duplicate Key Errors
 --error 1022, ER_DUP_ENTRY
@@ -109,8 +116,8 @@ sync_slave_with_master;
 --echo #
 
 connection master;
-create table t1(a int auto_increment, key(a));
-create table t2(a int);
+eval create table t1(a int auto_increment, key(a)) engine=$engine_type;
+eval create table t2(a int) engine=$engine_type;
 insert into t1 (a) values (null);
 insert into t2 (a) select a from t1 where a is null;
 insert into t2 (a) select a from t1 where a is null;
@@ -139,11 +146,11 @@ drop function if exists bug15728_insert;
 drop table if exists t1, t2;
 --enable_warnings
 
-create table t1 (
+eval create table t1 (
   id int not null auto_increment,
   last_id int,
   primary key (id)
-);
+) engine=$engine_type;
 create function bug15728() returns int(11)
   return last_insert_id();
 
@@ -152,11 +159,11 @@ insert into t1 (last_id) values (last_insert_id());
 insert into t1 (last_id) values (bug15728());
 
 # Check that nested call replicates too.
-create table t2 (
+eval create table t2 (
   id int not null auto_increment,
   last_id int,
   primary key (id)
-);
+) engine=$engine_type;
 delimiter |;
 create function bug15728_insert() returns int(11) modifies sql data
 begin
@@ -215,8 +222,8 @@ drop procedure foo;
 # test of BUG#20188 REPLACE or ON DUPLICATE KEY UPDATE in
 # auto_increment breaks binlog
 
-create table t1 (n int primary key auto_increment not null,
-b int, unique(b));
+eval create table t1 (n int primary key auto_increment not null,
+                      b int, unique(b)) engine=$engine_type;
 
 # First, test that we do not call restore_auto_increment() too early
 # in write_record():
@@ -257,8 +264,8 @@ select * from t1 order by n;
 # and now test for the bug:
 connection master;
 drop table t1;
-create table t1 (n int primary key auto_increment not null,
-b int, unique(b));
+eval create table t1 (n int primary key auto_increment not null,
+                      b int, unique(b)) engine=$engine_type;
 insert into t1 values(null,100);
 select * from t1 order by n;
 sync_slave_with_master;
@@ -282,29 +289,29 @@ sync_slave_with_master;
 
 connection master;
 # testcase with INSERT VALUES
-CREATE TABLE t1 (a INT NOT NULL PRIMARY KEY AUTO_INCREMENT, b INT,
-UNIQUE(b));
+eval CREATE TABLE t1 (a INT NOT NULL PRIMARY KEY AUTO_INCREMENT, b INT,
+                      UNIQUE(b)) ENGINE=$engine_type;
 INSERT INTO t1(b) VALUES(1),(1),(2) ON DUPLICATE KEY UPDATE t1.b=10;
-SELECT * FROM t1;
+SELECT * FROM t1 ORDER BY a;
 sync_slave_with_master;
-SELECT * FROM t1;
+SELECT * FROM t1 ORDER BY a;
 connection master;
 drop table t1;
 
 # tescase with INSERT SELECT
-CREATE TABLE t1 (
+eval CREATE TABLE t1 (
   id bigint(20) unsigned NOT NULL auto_increment,
   field_1 int(10) unsigned NOT NULL,
   field_2 varchar(255) NOT NULL,
   field_3 varchar(255) NOT NULL,
   PRIMARY KEY (id),
   UNIQUE KEY field_1 (field_1, field_2)
-);
-CREATE TABLE t2 (
+) ENGINE=$engine_type;
+eval CREATE TABLE t2 (
   field_a int(10) unsigned NOT NULL,
   field_b varchar(255) NOT NULL,
   field_c varchar(255) NOT NULL
-);
+) ENGINE=$engine_type;
 INSERT INTO t2 (field_a, field_b, field_c) VALUES (1, 'a', '1a');
 INSERT INTO t2 (field_a, field_b, field_c) VALUES (2, 'b', '2b');
 INSERT INTO t2 (field_a, field_b, field_c) VALUES (3, 'c', '3c');
@@ -324,9 +331,9 @@ SELECT t2.field_a, t2.field_b, t2.field_c
 FROM t2
 ON DUPLICATE KEY UPDATE
 t1.field_3 = t2.field_c;
-SELECT * FROM t1;
+SELECT * FROM t1 ORDER BY id;
 sync_slave_with_master;
-SELECT * FROM t1;
+SELECT * FROM t1 ORDER BY id;
 connection master;
 drop table t1, t2;
 
@@ -348,17 +355,17 @@ DROP TABLE IF EXISTS t1, t2;
 # Reset result of LAST_INSERT_ID().
 SELECT LAST_INSERT_ID(0);
 
-CREATE TABLE t1 (
+eval CREATE TABLE t1 (
   id INT NOT NULL DEFAULT 0,
   last_id INT,
   PRIMARY KEY (id)
-);
+) ENGINE=$engine_type;
 
-CREATE TABLE t2 (
+eval CREATE TABLE t2 (
   id INT NOT NULL AUTO_INCREMENT,
   last_id INT,
   PRIMARY KEY (id)
-);
+) ENGINE=$engine_type;
 
 delimiter |;
 CREATE PROCEDURE p1()
@@ -369,12 +376,12 @@ END|
 delimiter ;|
 
 CALL p1();
-SELECT * FROM t1;
-SELECT * FROM t2;
+SELECT * FROM t1 ORDER BY id;
+SELECT * FROM t2 ORDER BY id;
 
 sync_slave_with_master;
-SELECT * FROM t1;
-SELECT * FROM t2;
+SELECT * FROM t1 ORDER BY id;
+SELECT * FROM t2 ORDER BY id;
 
 connection master;
 
@@ -394,11 +401,11 @@ DROP FUNCTION IF EXISTS f3;
 DROP TABLE IF EXISTS t1, t2;
 --enable_warnings
 
-CREATE TABLE t1 (
+eval CREATE TABLE t1 (
     i INT NOT NULL AUTO_INCREMENT PRIMARY KEY,
     j INT DEFAULT 0
-);
-CREATE TABLE t2 (i INT);
+) ENGINE=$engine_type;
+eval CREATE TABLE t2 (i INT) ENGINE=$engine_type;
 
 delimiter |;
 CREATE PROCEDURE p1()
@@ -443,14 +450,16 @@ UPDATE t1 SET j= -1 WHERE i IS NULL;
 # Test statement-based replication of function calls.
 INSERT INTO t1 (i) VALUES (NULL);
 
+# Here, we rely on having set @@concurrent_insert= 0 (see comment at
+# the top of this file).
 connection master1;
 INSERT INTO t1 (i) VALUES (NULL);
 
 connection master;
 SELECT f3();
 
-SELECT * FROM t1;
-SELECT * FROM t2;
+SELECT * FROM t1 ORDER BY i;
+SELECT * FROM t2 ORDER BY i;
 
 sync_slave_with_master;
 SELECT * FROM t1;
@@ -472,11 +481,11 @@ sync_slave_with_master;
 
 # Tests in this file are tightly bound together.  Recreate t2.
 connection master;
-create table t2 (
+eval create table t2 (
   id int not null auto_increment,
   last_id int,
   primary key (id)
-);
+) engine=$engine_type;
 
 
 # Test for BUG#20341 "stored function inserting into one
@@ -484,7 +493,8 @@ create table t2 (
 
 connection master;
 truncate table t2;
-create table t1 (id tinyint primary key); # no auto_increment
+# no auto_increment
+eval create table t1 (id tinyint primary key) engine=$engine_type;
 
 delimiter |;
 create function insid() returns int
@@ -504,20 +514,20 @@ insert into t2 (id) values(5),(6),(7);
 delete from t2 where id>=5;
 set sql_log_bin=1;
 insert into t1 select insid();
-select * from t1;
-select * from t2;
+select * from t1 order by id;
+select * from t2 order by id;
 
 sync_slave_with_master;
-select * from t1;
-select * from t2;
+select * from t1 order by id;
+select * from t2 order by id;
 
 connection master;
 drop table t1;
 drop function insid;
 
 truncate table t2;
-create table t1 (n int primary key auto_increment not null,
-b int, unique(b));
+eval create table t1 (n int primary key auto_increment not null,
+                      b int, unique(b)) engine=$engine_type;
 delimiter |;
 create procedure foo()
 begin
@@ -528,14 +538,15 @@ begin
 end|
 delimiter ;|
 call foo();
-select * from t1;
-select * from t2;
+select * from t1 order by n;
+select * from t2 order by id;
 
 sync_slave_with_master;
-select * from t1;
-select * from t2;
+select * from t1 order by n;
+select * from t2 order by id;
 
 connection master;
 drop table t1, t2;
 drop procedure foo;
+SET @@global.concurrent_insert= @old_concurrent_insert;
 sync_slave_with_master;
diff --git a/mysql-test/suite/rpl/r/rpl_insert_id.result b/mysql-test/suite/rpl/r/rpl_insert_id.result
index b0c1b6cfd73..3aa92009f5e 100644
--- a/mysql-test/suite/rpl/r/rpl_insert_id.result
+++ b/mysql-test/suite/rpl/r/rpl_insert_id.result
@@ -15,8 +15,8 @@ reset master;
 reset slave;
 drop table if exists t1,t2,t3,t4,t5,t6,t7,t8,t9;
 start slave;
-create table t1(a int auto_increment, key(a));
-create table t2(b int auto_increment, c int, key(b));
+create table t1(a int auto_increment, key(a)) engine=innodb;
+create table t2(b int auto_increment, c int, key(b)) engine=innodb;
 insert into t1 values (1),(2),(3);
 insert into t1 values (null);
 insert into t2 values (null,last_insert_id());
@@ -54,8 +54,8 @@ b	c
 #
 drop table t2;
 drop table t1;
-create table t1(a int auto_increment, key(a));
-create table t2(b int auto_increment, c int, key(b));
+create table t1(a int auto_increment, key(a)) engine=innodb;
+create table t2(b int auto_increment, c int, key(b)) engine=innodb;
 insert into t1 values (10);
 insert into t1 values (null),(null),(null);
 insert into t2 values (5,0);
@@ -87,7 +87,7 @@ drop table t2;
 #           FOREIGN_KEY_CHECKS
 #
 SET TIMESTAMP=1000000000;
-CREATE TABLE t1 ( a INT UNIQUE );
+CREATE TABLE t1 ( a INT UNIQUE ) engine=innodb;
 SET FOREIGN_KEY_CHECKS=0;
 INSERT INTO t1 VALUES (1),(1);
 Got one of the listed errors
@@ -95,8 +95,8 @@ drop table t1;
 #
 # Bug#14553: NULL in WHERE resets LAST_INSERT_ID
 #
-create table t1(a int auto_increment, key(a));
-create table t2(a int);
+create table t1(a int auto_increment, key(a)) engine=innodb;
+create table t2(a int) engine=innodb;
 insert into t1 (a) values (null);
 insert into t2 (a) select a from t1 where a is null;
 insert into t2 (a) select a from t1 where a is null;
@@ -123,7 +123,7 @@ create table t1 (
 id int not null auto_increment,
 last_id int,
 primary key (id)
-);
+) engine=innodb;
 create function bug15728() returns int(11)
 return last_insert_id();
 insert into t1 (last_id) values (0);
@@ -133,7 +133,7 @@ create table t2 (
 id int not null auto_increment,
 last_id int,
 primary key (id)
-);
+) engine=innodb;
 create function bug15728_insert() returns int(11) modifies sql data
 begin
 insert into t2 (last_id) values (bug15728());
@@ -199,7 +199,7 @@ drop function bug15728_insert;
 drop table t1,t2;
 drop procedure foo;
 create table t1 (n int primary key auto_increment not null,
-b int, unique(b));
+b int, unique(b)) engine=innodb;
 set sql_log_bin=0;
 insert into t1 values(null,100);
 replace into t1 values(null,50),(null,100),(null,150);
@@ -243,7 +243,7 @@ n	b
 1001	600
 drop table t1;
 create table t1 (n int primary key auto_increment not null,
-b int, unique(b));
+b int, unique(b)) engine=innodb;
 insert into t1 values(null,100);
 select * from t1 order by n;
 n	b
@@ -264,13 +264,13 @@ n	b
 3	350
 drop table t1;
 CREATE TABLE t1 (a INT NOT NULL PRIMARY KEY AUTO_INCREMENT, b INT,
-UNIQUE(b));
+UNIQUE(b)) ENGINE=innodb;
 INSERT INTO t1(b) VALUES(1),(1),(2) ON DUPLICATE KEY UPDATE t1.b=10;
-SELECT * FROM t1;
+SELECT * FROM t1 ORDER BY a;
 a	b
 1	10
 2	2
-SELECT * FROM t1;
+SELECT * FROM t1 ORDER BY a;
 a	b
 1	10
 2	2
@@ -282,12 +282,12 @@ field_2 varchar(255) NOT NULL,
 field_3 varchar(255) NOT NULL,
 PRIMARY KEY (id),
 UNIQUE KEY field_1 (field_1, field_2)
-);
+) ENGINE=innodb;
 CREATE TABLE t2 (
 field_a int(10) unsigned NOT NULL,
 field_b varchar(255) NOT NULL,
 field_c varchar(255) NOT NULL
-);
+) ENGINE=innodb;
 INSERT INTO t2 (field_a, field_b, field_c) VALUES (1, 'a', '1a');
 INSERT INTO t2 (field_a, field_b, field_c) VALUES (2, 'b', '2b');
 INSERT INTO t2 (field_a, field_b, field_c) VALUES (3, 'c', '3c');
@@ -304,7 +304,7 @@ SELECT t2.field_a, t2.field_b, t2.field_c
 FROM t2
 ON DUPLICATE KEY UPDATE
 t1.field_3 = t2.field_c;
-SELECT * FROM t1;
+SELECT * FROM t1 ORDER BY id;
 id	field_1	field_2	field_3
 1	1	a	1a
 2	2	b	2b
@@ -312,7 +312,7 @@ id	field_1	field_2	field_3
 4	4	d	4d
 5	5	e	5e
 6	6	f	6f
-SELECT * FROM t1;
+SELECT * FROM t1 ORDER BY id;
 id	field_1	field_2	field_3
 1	1	a	1a
 2	2	b	2b
@@ -330,28 +330,28 @@ CREATE TABLE t1 (
 id INT NOT NULL DEFAULT 0,
 last_id INT,
 PRIMARY KEY (id)
-);
+) ENGINE=innodb;
 CREATE TABLE t2 (
 id INT NOT NULL AUTO_INCREMENT,
 last_id INT,
 PRIMARY KEY (id)
-);
+) ENGINE=innodb;
 CREATE PROCEDURE p1()
 BEGIN
 INSERT INTO t2 (last_id) VALUES (LAST_INSERT_ID());
 INSERT INTO t1 (last_id) VALUES (LAST_INSERT_ID());
 END|
 CALL p1();
-SELECT * FROM t1;
+SELECT * FROM t1 ORDER BY id;
 id	last_id
 0	1
-SELECT * FROM t2;
+SELECT * FROM t2 ORDER BY id;
 id	last_id
 1	0
-SELECT * FROM t1;
+SELECT * FROM t1 ORDER BY id;
 id	last_id
 0	1
-SELECT * FROM t2;
+SELECT * FROM t2 ORDER BY id;
 id	last_id
 1	0
 DROP PROCEDURE p1;
@@ -364,8 +364,8 @@ DROP TABLE IF EXISTS t1, t2;
 CREATE TABLE t1 (
 i INT NOT NULL AUTO_INCREMENT PRIMARY KEY,
 j INT DEFAULT 0
-);
-CREATE TABLE t2 (i INT);
+) ENGINE=innodb;
+CREATE TABLE t2 (i INT) ENGINE=innodb;
 CREATE PROCEDURE p1()
 BEGIN
 INSERT INTO t1 (i) VALUES (NULL);
@@ -401,11 +401,14 @@ INSERT INTO t1 VALUES (NULL, LAST_INSERT_ID()), (NULL, LAST_INSERT_ID(5)),
 INSERT INTO t1 VALUES (NULL, 0), (NULL, LAST_INSERT_ID());
 UPDATE t1 SET j= -1 WHERE i IS NULL;
 INSERT INTO t1 (i) VALUES (NULL);
+SET @old_concurrent_insert= @@global.concurrent_insert;
+SET @@global.concurrent_insert= 0;
 INSERT INTO t1 (i) VALUES (NULL);
 SELECT f3();
 f3()
 0
-SELECT * FROM t1;
+SET @@global.concurrent_insert= @old_concurrent_insert;
+SELECT * FROM t1 ORDER BY i;
 i	j
 1	-1
 2	0
@@ -427,7 +430,7 @@ i	j
 18	14
 19	0
 20	0
-SELECT * FROM t2;
+SELECT * FROM t2 ORDER BY i;
 i
 2
 3
@@ -475,9 +478,9 @@ create table t2 (
 id int not null auto_increment,
 last_id int,
 primary key (id)
-);
+) engine=innodb;
 truncate table t2;
-create table t1 (id tinyint primary key);
+create table t1 (id tinyint primary key) engine=innodb;
 create function insid() returns int
 begin
 insert into t2 (last_id) values (0);
@@ -495,17 +498,17 @@ insert into t2 (id) values(5),(6),(7);
 delete from t2 where id>=5;
 set sql_log_bin=1;
 insert into t1 select insid();
-select * from t1;
+select * from t1 order by id;
 id
 0
-select * from t2;
+select * from t2 order by id;
 id	last_id
 4	0
 8	0
-select * from t1;
+select * from t1 order by id;
 id
 0
-select * from t2;
+select * from t2 order by id;
 id	last_id
 4	0
 8	0
@@ -513,7 +516,7 @@ drop table t1;
 drop function insid;
 truncate table t2;
 create table t1 (n int primary key auto_increment not null,
-b int, unique(b));
+b int, unique(b)) engine=innodb;
 create procedure foo()
 begin
 insert into t1 values(null,10);
@@ -522,16 +525,16 @@ insert ignore into t1 values(null,10);
 insert into t2 values(null,3);
 end|
 call foo();
-select * from t1;
+select * from t1 order by n;
 n	b
 1	10
-select * from t2;
+select * from t2 order by id;
 id	last_id
 1	3
-select * from t1;
+select * from t1 order by n;
 n	b
 1	10
-select * from t2;
+select * from t2 order by id;
 id	last_id
 1	3
 drop table t1, t2;