In calculating power, preliminary estimates of effect-size are needed. In low-dimensional problems, estimating effect-size from preliminary data can generally be done simply, and without significant bias. However, in high-throughput experiments, usual estimates of effect-size (as from eg. t-tests, regressions, etc.) result in a large (and somewhat unintuitive) bias. Calculating power using those biased effect-size-estimates results in an over-estimation of power. In this talk, we discuss a framework for using empirical Bayes and/or resampling to get a more accurate estimate of power --- these ideas are related to Stein shrinkage. We discuss this framework primarily in the case of high throughput screening (though it can apply more generally).