I analyze job search models with random layoffs in which employment opportunities are characterized by a wage and some measure of risk. Intuition suggests that a worker ought to demand a higher wage if he is to accept a job with a higher layoff rate; but this is not true in several models analyzed in the literature. I demonstrate here that assumptions about what happens immediately after a layoff and after a quit are critical in determining the relation between reservation wages and risk. Making these assumptions explicit clarifies the reasons why different models imply quite different predictions.