covering a song

Just curious but when you guys as drummers have to cover a song previously done by a drummer do you try to copy what that drummer did or do you try to interpret it in your own way? A lot of times it's hard because you may not agree with what the previous drummer did or you may interpret the song differently but for the sake of the other band member who know the part with a certain drum part it's probaly in the band's best interest for you to copy the other drummer. So with this dilemma, what do you do?