In this paper, we prove lower bounds for a large class of Subset Cover schemes (including all existing schemes based on pseudorandom sequence generators). In particular, we show that -For small r, bandwidth is Ω(r) -For some r, bandwidth is Ω(n/ log(s)) -For large r, bandwidth is n − r where n is the number of users, r is the number of revoked users, and s is the space required per user. These bounds are all tight in the sense that they match known constructions up to small constants.