The limited supply of vaccines against SARS-CoV-2 raises the question of targeted vaccination. Older and more sensitive hosts should be vaccinated first to minimize the disease burden. But what are the evolutionary consequences of targeted vaccination? We clarify the consequences of different vaccination strategies through the analysis of the speed of viral adaptation measured as the rate of change of the frequency of vaccine-escape mutations. We show that a vaccine-escape mutant is expected to

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... spread faster if vaccination targets individuals which are likely to be involved in a higher number of contacts. We also discuss the pros and cons of dose-sparing strategies. Because delaying the second dose increases the proportion of the population vaccinated with a single dose, this strategy can both speed-up the spread of the vaccine-escape mutant and reduce the cumulated number of deaths. Hence, slowing down viral adaptation may not always be the optimal vaccination strategy. We contend that a careful assessment of the consequences of alternative vaccination strategies on both (i) the speed of adaptation and (ii) the mortality is required to determine which individuals should be vaccinated first.