Before revision:  Specialising to the bacterial persister phenotype, we analyse stochastic switching between phenotypes in detail in an asymptotic limit . Abundant phenotypic variation tends to be linearly destabilising, but, surprisingly, a rare phenotype can have a stabilising effect.
After revision:  Specialising to the bacterial persister phenotype, we analyse stochastic switching between phenotypes in detail in an asymptotic limit and partly overturn classical stability paradigms: abundant phenotypic variation is linearly destabilizing but, surprisingly, a rare phenotype can have a stabilising effect.