The theory of adverse selection in insurance markets has been enormously influential among scholars, regulators, and the judiciary. But empirical support for adverse selection has been much less persuasive, and several recent studies have found little or no evidence of such selection in insurance markets. "Propitious" (advantageous) selection offers an alternative mechanism that is consistent with these empirical findings. Like adverse selection, the theory assumes that insureds have an informational advantage over insurers. However, propitious selection relies on the plausible assumption that risk aversion is negatively correlated with the riskiness or probability of loss across insureds - the more risk-averse are also the more careful, and hence are least likely to experience a loss. Theorists have recognized the possibility of equilibria in which highly risk averse insureds with a low probability of loss are willing to remain in the market, despite an actuarially unfair premium. But these conclusions derive from models with only two types of insureds. We use a simulation model that allows for flexible correlation between risk aversion and riskiness across a continuum of types, with plausible distributions of risk aversion and riskiness. We find that propitious selection alone can not preserve equilibrium in insurance markets. When insureds have moderate uncertainty about their own riskiness, however, equilibrium does become possible, albeit with considerable selection.