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Energy efficiency and power capping are critical concerns in server and cloud computing systems. They face growing challenges due to dynamic power variations from new client-directed web applications, as well as complex behaviors due to multicore resource sharing and hardware heterogeneity. This paper presents a new operating system facility called "power containers" that accounts for and controls the power and energy usage of individual fine-grained requests in multicore servers. This facility relies on three key techniques---1) online model that attributes multicore power (including shared maintenance power) to concurrently running tasks, 2) alignment of actual power measurements and model estimates to enable online model recalibration, and 3) on-the-fly application-transparent request tracking in multi-stage servers to isolate the power and energy contributions and customize per-request control. Our mechanisms enable new multicore server management capabilities including fair power capping that only penalizes power-hungry requests, and energy-aware request distribution between heterogeneous servers. Our evaluation uses three multicore processors (Intel Woodcrest, Westmere, and SandyBridge) and a variety of server and cloud computing (Google App Engine) workloads. Our results demonstrate the high accuracy of our request power accounting (no more than 11% errors) and the effectiveness of container-enabled power virus isolation and throttling. Our request distribution case study shows up to 25% energy saving compared to an alternative approach that recognizes machine heterogeneity but not fine-grained workload affinity.