Arbirarily varying channels (AVCs) are a model for communication under uncertain interference.  The assumption is that the interference in the channel is generated by an adversary, or jammer, who wishes to stymie communication between the transmitter and receiver.  This model is pessimistic and the corresponding capacities can be significantly lower than those for channels with stochastic noise.  This is because the interference can depend on the transmitted codeword.  In order to bridge this gap, two models which limit the adversary's knowledge of the transmitted codeword are proposed.  In the first, the adversary sees a delayed version of the transmitted codeword.  The capacity for this model is found under stochastic encoding for symmetric channels.  In the second model, the adversary sees a noisy version of the transmitted codeword.  The capacity for this model is found when the encoder and decoder share common randomness.