In this paper, we analyze the power consumption of different GPU-accelerated iterative solver implementations enhanced with energy-saving techniques. Specifically, while conducting kernel calls on the graphics accelerator, we manually set the host system to a power-efficient idle-wait status so as to leverage dynamic voltage and frequency control. While the usage of iterative refinement combined with mixed precision arithmetic often improves the execution time of an iterative solver on a graphics processor, this may not necessarily be true for the power consumption as well. To analyze the trade-off between computation time and power consumption we compare a plain GMRES solver and its preconditioned variant to the mixed-precision iterative refinement implementations based on the respective solvers. Benchmark experiments conclusively reveal how the usage of idle-wait during GPU-kernel calls effectively leverages the power-tools provided by hardware, and improves the energy performance of the algorithm.