Rothschild and Stiglitz (1976) examined primarily neutral insurance (non-redistributive) in a case of asymmetrical information. In their basic model, the insurer is unaware whether the insured is low or high-risk, and so the low-risk individuals have to shoulder an own risk that keeps high-risk individuals from presenting themselves as low-risk (second best solution). The authors also examine, in a model variant, optimum cross-subsidization, but this has been largely overlooked in the literature. This study extends the analysis to the cases of compulsory and redistributive insurance, and shows that for both types it is worth taking out full insurance, but everybody must pay for the average risk. In cases of great risk evasion or great damage, or of the presence of relatively few low-risk individuals, increases the utility not only for the high-risk type, but for the low-risk type as well: the second best redistribution Pareto-dominates the neutral solution.