Engineered underdominance (EU), meiotic drive (MD) and Wolbachia have been proposed as mechanisms for driving anti-pathogen transgenes into natural populations of insect vectors of human diseases. EU can drive transgenes to high and stable frequencies but requires the release of sizeable numbers of engineered insects. MD and Wolbachia either cannot maintain high frequencies of transgenes or lack appropriate expression in critical tissues, but both can drive the transgenes to spread from very low initial frequencies. Here we use mathematical models to assess the utility of combining EU with MD or with Wolbachia. Under some conditions, the combination of EU and MD results in a more efficient transgene-drive strategy than either mechanism alone. This combined strategy could drive the transgenes to stable fixation and would require fewer released insects than EU alone, especially when only males are released. However, a combination of EU and Wolbachia does not work better than EU alone because it requires the release of even more engineered insects.