Simple Query?

I am doing some optimization on our search, but I need some advise...

table: item

id name
--------------------------------------
1 iPod
2 Zune
3 Walkman

table: search_item

id_search id_item
--------------------------------------
1 1
1 2
1 3
2 2
2 3
3 1
3 3

Now what I want to have is the items that match with id_search 1 and
2 and 3. Therefore I use the following SQL query.

SELECT * FROM item WHERE id IN
(SELECT id_item FROM search_item WHERE id_search=1 AND id_item IN
(SELECT id_item FROM search_item WHERE id_search=2 AND id_item IN
(SELECT id_item FROM search_item WHERE id_search=3)));

This should only return id_item 3. Would this be the best SQL query
to get this result? I have the feeling there should be something
better, but I cannot find it. Anyone has a hint?