The Wyner interference network is a popular model used in research on cellular networks due to its simplicity and analytical tractability. In this paper, the optimal power allocation strategies in symmetric one- and two-sided Wyner models are investigated.We determine a sufficient condition for binary power control (BPC) to be optimal that can be applied to the one-sided symmetric model. We consider binary power schemes for the symmetric two-sided Wyner network. Using a method of grouping links and performing a piecewise comparison of the group rates, we are able to determine the optimal power policy that maximizes the network sum rate. The result of the optimization can be expressed as follows for both types of networks: When the interfering channel gain �ε is small, it is optimal (in the class of binary schemes) to have all links on; otherwise, alternate links are switched off to remove interference. We characterize the critical values of ε where the transitions occur. © 2014 IEEE.