This talk introduces a novel method for selecting main effects and a set of reparametrized predictors called conditional main effects (CMEs), which capture the conditional effect of a factor at a fixed level of another factor. CMEs represent interpretable, domain-specific phenomena for a wide range of applications in engineering, social sciences and genomics. The key challenge is in incorporating the grouped structure of CMEs within the variable selection procedure itself. We propose a new method, cmenet, which employs two principles (CME coupling and CME reduction) to effectively navigate the selection algorithm. Simulations demonstrate the improved performance of cmenet over generic variable selection methods. Applied to a gene association study on fly wing shape, cmenet not only provides more parsimonious models and improved predictive performance over existing methods, but also reveals important insights on gene activation behavior which can guide further experiments (joint with Simon Mak, paper in JASA Theory & Methods.)