Weconsider the problemof generic broadcast in asynchronous systems with crashes, a problem that was rst studied in 12]. Roughly speaking, given a \con ict" relation on the set of messages, generic broadcast ensures that any two messages that con ict are delivered in the same order messages that do not con ict may be delivered in di erent order. In this paper, we de ne what it means for an implementation generic broadcast to be \thrifty", and give corresponding implementations that are optimal in terms of resiliency. We also give an interesting application of our results regarding the implementation of atomic broadcast.