AccountName and ID from contactID

 Requirement: I am trying to get the acoountName of all cases which have contact with email adress as 'X'

The way I plan to implement it is by first getting the contactid's of all contacts with a 'X' as email address and then getting all cases for each of these contactId's and then getting AccountName on each of these cases. But this procedure seems to be very time consuming especially when we have large number of cases in database. I was wondering if there is a better and more efficient approach.

Thanks,

Saujanya