Optimization of data and acknowledgement (ACK) packets' transmission power levels is necessary to prolong the lifetime of wireless sensor networks (WSNs). Utilizing the maximum power level available results in the minimum level of handshake failures, however, such a strategy will also result in energy waste because it may not be necessary to utilize the maximum power level at each link. Alternatively, the optimal data and ACK packet transmission levels can be determined for each link that minimizes the energy cost of handshaking. Accomplishing this task requires that the packet failure rates for each combination of power levels for data and ACK packets are measured through a close loop scheme which brings extra overhead when compared to the strategy of employing the highest power level. In this paper, we propose a novel strategy based on random power level assignments that do not require the overhead necessary to measure the handshake failure rate, yet, at the same time performs better than the maximum power level assignment strategy. To evaluate the performance of the proposed strategy we built a novel mixed integer programming (MIP) framework. Our results show that random power assignment performs better than maximum power assignment in terms of network lifetime.