Recently, genetic strategies aimed at controlling populations of disease‐vectoring mosquitoes have received considerable attention as alternatives to traditional measures. Theoretical studies have shown that female‐killing (FK), antipathogen (AP), and reduce and replace (R&R) strategies can each decrease the number competent vectors. In this study, we utilize a mathematical model to evaluate impacts on competent Aedes aegypti populations of FK, AP, and R&R releases as well as hybrid strategies that result from combinations of these three approaches. We show that while the ordering of efficacy of these strategies depends upon population life history parameters, sex ratio of releases, and switch time in combination strategies, AP‐only and R&R/AP releases typically lead to the greatest long‐term reduction in competent vectors. R&R‐only releases are often less effective at long‐term reduction of competent vectors than AP‐only releases or R&R/AP releases. Furthermore, the reduction in competent vectors caused by AP‐only releases is easier to maintain than that caused by FK‐only or R&R‐only releases even when the AP gene confers a fitness cost. We discuss the roles that density dependence and inclusion of females play in the order of efficacy of the strategies. We anticipate that our results will provide added impetus to continue developing AP strategies.