Gene-environment-wide interaction studies of disease occurrence in human populations may be able to exploit the same agnostic approach to interrogating the human genome used by genome-wide association studies. The authors discuss 2 methods for taking advantage of possible independence between a single nucleotide polymorphism they call G (a genetic factor) and an environmental factor they call E while maintaining nominal type I error in studying G-E interaction when information on many genes is available. The first method is a simple 2-step procedure for testing the null hypothesis of no multiplicative interaction against the alternative hypothesis of a multiplicative interaction between an E and at least one of the markers genotyped in a genome-wide association study. The added power for the method derives from a clever work-around of a multiple testing procedure. The second is an empirical-Bayes-style shrinkage estimation framework for G-E interaction and the associated tests that can gain efficiency and power when the G-E independence assumption is met for most G's in the underlying population and yet, unlike the case-only method, is resistant to increased type I error when the underlying assumption of independence is violated. The development of new approaches to testing for interaction is an example of methodological progress leading to practical advantages.