Two strategies to control mosquito-borne diseases, such as malaria and dengue fever, are reducing mosquito population sizes or replacing populations with disease-refractory varieties. We propose a genetic system, Semele, which may be used for both. Semele consists of two components: a toxin expressed in transgenic males that either kills or renders infertile wild-type female recipients and an antidote expressed in females that protects them from the effects of the toxin. An all-male release results in population suppression because wild-type females that mate with transgenic males produce no offspring. A release that includes transgenic females results in gene drive since females carrying the allele are favored at high population frequencies. We use simple population genetic models to explore the utility of the Semele system. We find that Semele can spread under a wide range of conditions, all of which require a high introduction frequency. This feature is desirable since transgenic insects released accidentally are unlikely to persist, transgenic insects released intentionally can be spatially confined, and the element can be removed from a population through sustained release of wild-type insects. We examine potential barriers to Semele gene drive and suggest molecular tools that could be used to build the Semele system.