Binary power control has been shown to be optimal in a variety of network conditions. In the context of sumrate maximisation in interference networks, our main result states that the optimal power policy for a link is binary if it only interferes with one other link in the network. Examples of networks which have at least one link with this attribute include the two-link interference channel (IC), the one-sided Wyner network and the many-to-one interference channel. Previous works have fully characterised the optimal power scheme for the two-link IC and they agree with our results. For the one-sided Wyner network, our main result leads to a problem which is tractable and can be solved using dynamic programming methods.