The problem we address is how to communicate securely with a set of users (the target set) over an insecure broadcast channel. In order to solve this problem, several broadcast encryption schemes have been proposed. In these systems, the parameters of major concern are the length of transmission and number of keys held by each user's set top terminal (STT). Due to the need to withstand hardware tampering, the amount of secure memory available in the STTs is quite small, severely limiting the number of keys each user holds. In such cases, known theoretical bounds seem to indicate that non-trivial broadcast encryption schemes are only feasible when the number of users is small. In order to break away from these theoretical bounds, our approach is to allow a controlled number of users outside the target set to occasionally receive the multicast. This relaxation is appropriate for low-cost transmissions such as multicasting electronic coupons. For this purpose, we introduce f-redundant establishment key allocations, which guarantee that the total number of recipients is no more than f times the number of intended recipients. We measure the performance of such schemes by the number of transmissions they require, by their redundancy, and by their opportunity, which is the probability of a user outside the target set to be part of the multicast. We first prove a new lower bound and discuss the basic trade-offs associated with this new setting. Then we present several new f-redundant establishment key allocations. We evaluate the schemes' performance under all the relevant measures by extensive simulation. Our results indicate that, unlike previous solutions, it seems possible to design practical schemes in this new setting.