diff --git a/mysql-test/extra/binlog_tests/binlog_insert_delayed.test b/mysql-test/extra/binlog_tests/binlog_insert_delayed.test
index d073c8ef227..c99d0b86be3 100644
--- a/mysql-test/extra/binlog_tests/binlog_insert_delayed.test
+++ b/mysql-test/extra/binlog_tests/binlog_insert_delayed.test
@@ -1,17 +1,43 @@
-# Test of binlogging of INSERT_ID with INSERT DELAYED
+# ==== Purpose ====
+#
+# Verify that INSERT DELAYED in mixed or row mode writes events to the
+# binlog, and that AUTO_INCREMENT works correctly.
+#
+# ==== Method ====
+#
+# Insert both single and multiple rows into an autoincrement column,
+# both with specified value and with NULL.
+#
+# With INSERT DELAYED, the rows do not show up in the table
+# immediately, so we must do source include/wait_until_rows_count.inc
+# between any two INSERT DELAYED statements.  Moreover, if mixed or
+# row-based logging is used, there is also a delay between when rows
+# show up in the table and when they show up in the binlog.  To ensure
+# that the rows show up in the binlog, we call FLUSH TABLES, which
+# waits until the delayed_insert thread has finished.
+#
+# We cannot read the binlog after executing INSERT DELAYED statements
+# that insert multiple rows, because that is nondeterministic. More
+# precisely, rows may be written in batches to the binlog, where each
+# batch has one Table_map_log_event and one or more
+# Write_rows_log_event. The number of rows included in each batch is
+# nondeterministic.
+#
+# ==== Related bugs ====
+#
+# BUG#20627: INSERT DELAYED does not honour auto_increment_* variables
+# Bug in this test: BUG#38068: binlog_stm_binlog fails sporadically in pushbuild
+
+
 create table t1 (a int not null auto_increment, primary key (a)) engine=myisam;
-# First, avoid BUG#20627:
-set @@session.auto_increment_increment=1, @@session.auto_increment_offset=1;
-# Verify that only one INSERT_ID event is binlogged.
-# Note, that because of WL#3368 mixed mode binlog records RBR events for the delayed
+
 let $table=t1;
-let $rows_inserted=11; # total number of inserted rows in this test
+let $count=0;
+
 insert delayed into t1 values (207);
-let $count=1;
-
-# use this macro instead of sleeps.
-
+inc $count;
 --source include/wait_until_rows_count.inc
+
 insert delayed into t1 values (null);
 inc $count;
 --source include/wait_until_rows_count.inc
@@ -20,9 +46,10 @@ insert delayed into t1 values (300);
 inc $count;
 --source include/wait_until_rows_count.inc
 
-# moving binlog check affront of multi-rows queries which work is indeterministic (extra table_maps)
-# todo: better check is to substitute SHOW BINLOG with reading from binlog, probably bug#19459 is in
-# the way
+# It is not enough to wait until all rows have been inserted into the
+# table. FLUSH TABLES ensures that they are in the binlog too.  See
+# comment above.
+FLUSH TABLES;
 source include/show_binlog_events.inc;
 
 insert delayed into t1 values (null),(null),(null),(null);
@@ -33,8 +60,5 @@ insert delayed into t1 values (null),(null),(400),(null);
 inc $count; inc $count; inc $count; inc $count;
 --source include/wait_until_rows_count.inc
 
-#check this assertion about $count calculation
---echo $count == $rows_inserted
-
 select * from t1;
 drop table t1;
diff --git a/mysql-test/suite/binlog/r/binlog_stm_binlog.result b/mysql-test/suite/binlog/r/binlog_stm_binlog.result
index 20d7281d5cc..ae8c1e11737 100644
--- a/mysql-test/suite/binlog/r/binlog_stm_binlog.result
+++ b/mysql-test/suite/binlog/r/binlog_stm_binlog.result
@@ -629,10 +629,10 @@ master-bin.000001	#	Query	#	#	use `mysql`; UPDATE user SET password=password('An
 master-bin.000001	#	Query	#	#	use `mysql`; DELETE FROM user WHERE host='localhost' AND user='@#@'
 drop table t1,t2,t3,tt1;
 create table t1 (a int not null auto_increment, primary key (a)) engine=myisam;
-set @@session.auto_increment_increment=1, @@session.auto_increment_offset=1;
 insert delayed into t1 values (207);
 insert delayed into t1 values (null);
 insert delayed into t1 values (300);
+FLUSH TABLES;
 show binlog events from <binlog_start>;
 Log_name	Pos	Event_type	Server_id	End_log_pos	Info
 master-bin.000001	#	Query	#	#	use `test`; create table t1 (id tinyint auto_increment primary key)
@@ -660,9 +660,9 @@ master-bin.000001	#	Query	#	#	use `test`; BEGIN
 master-bin.000001	#	Table_map	#	#	table_id: # (test.t1)
 master-bin.000001	#	Write_rows	#	#	table_id: # flags: STMT_END_F
 master-bin.000001	#	Query	#	#	use `test`; COMMIT
+master-bin.000001	#	Query	#	#	use `test`; FLUSH TABLES
 insert delayed into t1 values (null),(null),(null),(null);
 insert delayed into t1 values (null),(null),(400),(null);
-11 == 11
 select * from t1;
 a
 207