This paper addresses the assignment of transmission and sleep time slots between interfering transmitters with the objective of minimal power consumption. In particular, we address the constructive alignment of Discontinuous Transmission (DTX) time slots under link rate constraints. Due to the complexity of the combinatorial optimization problem at hand, we resort to heuristic assignment strategies. We derive four time slot alignment solutions (sequential alignment, random alignment, p-persistent ranking and DTX alignment with memory) and identify trade-offs. One solution, DTX alignment with memory, addresses trade-offs of the other three by maintaining memory of past alignment and channel quality to buffer short term changes in channel quality. All strategies are found to exhibit similar convergence behavior, but different power consumption and retransmission probabilities. DTX alignment with memory is shown to achieve up to 40% savings in power consumption and more than 20% lower retransmission probability than the state of the art.