Power consumption is widely regarded as one of the biggest challenges to reaching the next generation of high performance computing. On future supercomputers, power will be a limited resource. This constraint will affect the performance of both simulation and visualization workloads. Understanding how a particular application behaves under a power limit is critical to making better use of the limited power. In this research, we focus specifically on visualization and analysis applications, which are an important component in HPC. Visualization algorithms merit special consideration, since they are more data intensive in nature than traditional HPC programs, such as simulation codes. We explore the power and performance tradeoffs for several common algorithms under different configurations, and understand how power constraints will affect execution behaviors. We then demonstrate that we can gain additional performance by redistributing power based on performance predictions provided by the visualization algorithm.