The ability of microbial populations to increase fitness through fixation of mutants with an increased growth rate has been well described. In experimental studies, this is often the only way fitness can be increased. In natural settings, however, fitness can also be improved by increasing the ability of the microbe to transmit from one host to the next. For many pathogens, transmission includes a phase outside the host during which they need to survive before the chance of reinfecting a new host occurs. In such a situation, a reduced death rate during this phase will lead to improved fitness. Here, we compute the fixation probability of mutants that better survive the transmission bottleneck during the evolution of microbial populations. We derive analytical results that show that transmission mutants are often likely to occur and that their importance relative to growth mutants increases as the population decline during the transmission phase increases. We confirm our theoretical results with numerical simulations and suggest specific experiments that can be done to test our predictions.