Consolidation of workloads has emerged as a key mechanism to dampen the rapidly growing energy expenditure within enterprise-scale data centers. To gainfully utilize consolidation-based techniques, we must be able to characterize the power consumption of groups of co-located applications. Such characterization is crucial for effective prediction and enforcement of appropriate limits on power consumption - power budgets - within the data center. We identify two kinds of power budgets (i) an average budget to capture an upper bound on long-term energy consumption within that level and (ii) a sustained budget to capture any restrictions on sustained draw of current above a certain threshold. Using a simple measurement infrastructure, we derive power profiles - statistical descriptions of the power consumption of applications. Based on insights gained from detailed profiling of several applications - both individual and consolidated - we develop models for predicting average and sustained power consumption of consolidated applications. We conduct an experimental evaluation of our techniques on a Xen-based server that consolidates applications drawn from a diverse pool. For a variety of consolidation scenarios, We are able to predict average power consumption within 5% error margin and sustained power within 10% error margin. Our sustained power prediction techniques allow us to predict close yet safe upper bounds on the sustained power consumption of consolidated applications.