Shared resource contention has been a major performance issue for CMPs. In this paper we focus on power, which is one of the most valuable shared resources of CMPs. We believe it is important to study power contention, especially with the prevalence of power capping features among modern commercial microprocessors. When multiple processes compete for power in such systems, the power management system attempts to mitigate the contention (i.e., reduce the power consumption) by slowing down the processor, which results in degraded total system performance. We characterize this phenomenon using a real testbed with an Intel processor with power capping capability realized by the RAPL technology. We observe noticeable performance degradation for SPEC CPU2006, especially at tighter power caps. In order to solve this problem, we develop a shared resourceaware scheduling algorithm that improves system performance by mitigating the contention for power and the shared memory subsystem at the same time. Evaluation results across a variety of multiprogrammed workloads show performance improvements over a state-of-the-art scheduling policy which only considers memory subsystem contention. In addition, we present a guard mechanism implemented on top of the proposed scheduler that greatly improves performance when there is severe power contention that introduces performance anomalies.