Data centers can lower costs significantly by provisioning expensive electrical equipment (such as UPS, diesel generators, and cooling capacity) for the actual peak power consumption rather than server nameplate power ratings. However, it is possible that this under-provisioned power level is exceeded due to software behaviors on rare occasions and could cause the entire data center infrastructure to breach the safety limits. A mechanism to cap servers to stay within the provisioned budget is needed, and processor frequency scaling based power capping methods are readily available for this purpose. We show that existing methods, when applied across a large number of servers, are not fast enough to operate correctly under rapid power dynamics observed in data centers. We also show that existing methods when applied to an open system (where demand is independent of service rate) can cause cascading failures in the software service hosted, causing the service performance to fall uncontrollably even when power capping is applied for only a small reduction in power consumption. We discuss the causes for both these short-comings and point out techniques that can yield a safe, fast, and stable power capping solution. Our techniques use admission control to limit power consumption and ensure stability, resulting in orders of magnitude improvement in performance. We also discuss why admission control cannot replace existing power capping methods but must be combined with them.