Power-aware computing has emerged as a significant concern in data centers. In this work, we develop empirical models for estimating the power consumed by web servers. These models can be used by on-the-fly power-saving algorithms and are imperative for simulators that evaluate the power behavior of workloads. To apply power saving methodologies and algorithms at the data center level, we must first be able to measure or estimate the power and performance of individual servers running in the data centers. We show a novel method for developing full system web server power models that reduces non-linear relationships among performance measurements and system power and prunes model parameters. The web server power models use as parameters performance indicators read from the machine internal performance counters. We evaluate our approach on an AMD Opteron-based web server and on an Intel i7-based web sever. Our best model displays an average absolute error of 1.92 % for Intel i7 server and 1.46 % for AMD Opteron as compared to actual measurements, and 90th percentile for the absolute percent error equals to 2.66 % for Intel i7 and 2.08 % for AMD Opteron.