Scheduling of transmissions is one of the most fundamental problems in the context of wireless networks. In this article, we consider the problem of computing power efficient schedules with high throughput. We answer the open question concerning the complexity of scheduling with power control in the SINRG model of interference. Based on a novel scheme for dynamic computation of optimum transmission powers in feasible schedules, we introduce a new and efficient heuristic for finding good schedules along the tradeoff between throughput and energy efficiency in the physical SINR model. Since our algorithms do not rely on simplistic assumptions about path loss, they are suited for realistic scenarios with attenuation and shadowing effects. We compare our approach to a broad selection of state-of-the-art approaches in indoor and outdoor scenarios. In all situations, our approach outperforms the existing approaches with respect to schedule length and power consumption, i. e., yields paretosuperior schedules including schedules that significantly improve the throughput.