Autocommit off and transaction isolation level

Hi all,

I have come across some weird behavior in postgres concerning autocommit=off
and setting the transaction isolation level. I have no explanation why
things should work as they do, so I consider this a bug, no?

With autocommit=on and normal begin; ... commit; block setting the
transaction isolation level works fine:

billing=# begin;
BEGIN
billing=# set transaction isolation level serializable;
SET
billing=# show transaction isolation level;
TRANSACTION ISOLATION LEVEL
-----------------------------
SERIALIZABLE
(1 row)

billing=# commit;
COMMIT

Now setting autocommit=off the set transaction isolation level command does
not show any effect:

billing=# set autocommit to off;
SET
billing=# set transaction isolation level serializable;
SET
billing=# select current_date;
date
------------
2003-01-02
(1 row)

billing=# show transaction isolation level;
TRANSACTION ISOLATION LEVEL
-----------------------------
READ COMMITTED <---- this should be SERIALIZABLE, no??
(1 row)

billing=# commit;
COMMIT

Is it a bug?
Regards,
Michael Paesold