Mysql optimization for select query with IN() clause inside where clause (explain output given)

Question

I have this query:-

SELECT SUM(DISTINCT( ttagrels.id_tag IN ( 1816, 2642, 1906, 1398,
                                          2436, 2940, 1973, 2791, 1389 ) )) AS
       key_1_total_matches,
       IF(( od.id_od > 0 ), COUNT(DISTINCT( od.id_od )), 0)                 AS
       tutor_popularity,
       td.*,
       u.*
FROM   tutor_details AS td
       JOIN users AS u
         ON u.id_user = td.id_user
       JOIN all_tag_relations AS ttagrels
         ON td.id_tutor = ttagrels.id_tutor
       LEFT JOIN learning_packs AS lp
         ON ttagrels.id_lp = lp.id_lp
       LEFT JOIN learning_packs_categories AS lpc
         ON lpc.id_lp_cat = lp.id_lp_cat
       LEFT JOIN learning_packs_categories AS lpcp
         ON lpcp.id_lp_cat = lpc.id_parent
       LEFT JOIN learning_pack_content AS lpct
         ON ( lp.id_lp = lpct.id_lp )
       LEFT JOIN webclasses AS wc
         ON ttagrels.id_wc = wc.id_wc
       LEFT JOIN learning_packs_categories AS wcc
         ON wcc.id_lp_cat = wc.id_wp_cat
       LEFT JOIN learning_packs_categories AS wccp
         ON wccp.id_lp_cat = wcc.id_parent
       LEFT JOIN order_details AS od
         ON td.id_tutor = od.id_author
       LEFT JOIN orders AS o
         ON od.id_order = o.id_order
WHERE  ( u.country = 'IE'
          OR u.country IN ( 'INT' ) )
       AND u.status = 1
       AND CASE
             WHEN ( lp.id_lp > 0 ) THEN lp.id_status = 1
                                        AND lp.published = 1
                                        AND lpcp.status = 1
                                        AND ( lpcp.country_code = 'IE'
                                               OR lpcp.country_code IN ( 'INT' )
                                            )
             ELSE 1
           END
       AND CASE
             WHEN ( wc.id_wc > 0 ) THEN wc.wc_api_status = 1
                                        AND wc.id_status = 1
                                        AND wc.wc_type = 0
                                        AND
             wc.class_date > '2010-06-16 11:44:40'
                                        AND wccp.status = 1
                                        AND ( wccp.country_code = 'IE'
                                               OR wccp.country_code IN ( 'INT' )
                                            )
             ELSE 1
           END
       AND CASE
             WHEN ( od.id_od > 0 ) THEN od.id_author = td.id_tutor
                                        AND o.order_status = 'paid'
                                        AND CASE
             WHEN ( od.id_wc > 0 ) THEN od.can_attend_class = 1
             ELSE 1
                                            END
             ELSE 1
           END
       AND ( ttagrels.id_tag IN ( 1816, 2642, 1906, 1398,
                                  2436, 2940, 1973, 2791, 1389 ) )
GROUP  BY td.id_tutor
HAVING key_1_total_matches = 1
ORDER  BY tutor_popularity DESC,
          u.surname ASC,
          u.name ASC
LIMIT  0, 20 

The numbers inside the IN() are actually ids of another table called Tags which matched the search keywords entered by users. In this example the user has searched "class".

See the explain output of this query here:- http://www.test.examvillage.com/Screenshot.png

The time taken by this query is 0.0536 sec

But, if the number of values in the ttagrels.id_tag in () increases (as user enters more search keywords), the execution time rises to around 1-5 seconds and more.For example, if user searched "class Available to tutors and students 3 times a day"
the execution time is 4.2226 sec. The explain query output for this query contains 2513 under rows.

There are a total of 6,152 records in the All_Tag_Relations table. Is any further optimization possible?