Return LEFT JOINed tables when one has no matching column

Hi all,

I've got a variation on a question I asked some time ago... I've got
a table that is simply a collection of "variable" -> "value" columns
with a pointer to another table. I use this as little as possible, given
how much of a headache it is, but I've run into a situation where I need
to pull something from it in a JOIN query. Trick is, the column
'variable' may simply not exist, but I want the rest of the query to
return and let it be NULL.

Specifically, I've got a query like this:

SELECT
a.tbl1_name,
b.tbl2_date,
c.tbl3_value AS some_value
FROM
table_1 a
LEFT JOIN
table_2 b ON (a.tbl1_id=b.tbl2_tbl1_id)
LEFT JOIN
table_3 c ON (a.tbl1_id=c.tbl3_tbl1_id)
WHERE
c.tbl3_variable='some_variable'
AND
a.tbl1_id=123;

I want the data from table_1 and table_2 to return and table_3 to
return NULL when there is no matching c.tbl3_variable='some_variable'.
Is this possible?

Thanks as always!

Madi