When the signs of the βC1×EσC1,GσG2 or the βG×C1σC1,EσE2 terms are opposite the sign of the βG×E term, properly controlling for covariates can increase power to detect true G×E interactions. However, when those terms are of the same sign as the βG×E term, properly controlling for covariates will weaken evidence for apparent G×E interactions.