Optimizing a query with group by and order by count

[mansup kulel]

Hi,
I've a table which has millions of records
the table has cat columin which is varchar(250) NOT NULl and has index

i'm trying to optimize this query

SELECT `SIC`, COUNT(`SIC`) as total FROM `listing` GROUP BY `SIC` HAVING `total` > 1 ORDER BY `total` DESC LIMIT 0, 200

it takes about 2.5 secs to execute and uses index, temporary tbl and filesort but without the order by statement it only takes about 0.05 sec only using index

now could you please suggest me what should i do to get the least execution time with the order by statement.

Thank you very much for your time.