Most information-theoretic analyses of communication systems with feedback assume perfect output feedback. For multiaccess channels, this feedback can enable cooperation between users. However, as shown by a simple example, the rate required by the feedback link may exceed the capacity gains in the forward link. It is therefore of interest to look at systems where the feedback is rate-limited. For the compound multiaccess channel zero-rate feedback can tune the communication system to the realized channel, but for discrete memoryless channel the capacity region under zero-rate feedback is the same as that without feedback.