We seek to understand the conditions favoring the evolution of acute, highly transmissible infections. Most work on the life-history evolution of pathogens has focused on the transmission-virulence trade-off. Here we focus on a distinct trade-off that operates, even among avirulent pathogens, between a pathogen's speed of invasion and its ability to persist in a finite host population. Other authors have shown how this invasion-persistence trade-off can lead to intermediate pathogen attack rates but have done so only by imposing trade-offs between the pathogen's transmissibility and the duration of the infectious period. Here we delve deeper, by linking a model of within-host pathogen dynamics-in which pathogen life-history parameters figure directly-to an epidemiological model at the population level. We find that a key determinant of the evolutionary trajectory is the shape of the dose-response curve that relates within-host pathogen load to between-host transmission. In particular, under the usual assumption of proportionality we find that pathogens tend to evolve to the edge of their own extinction. Under more realistic assumptions, a critical host population size exists, above which highly acute pathogens are buffered from extinction. Our study is motivated by the emergence of acuteness in two human pathogens, Bordetella pertussis and Bordetella parapertussis, which independently evolved from an ancestor, Bordetella bronchiseptica, characterized by chronic (nonacute) infection of wildlife. In contrast to the plethora of models that predict evolution of more aggressive pathogens in larger or denser populations, the invasion-persistence trade-off also operates for frequency-dependent pathogens.