We study an adverse-selection insurance economy in which consumers can purchase coverage from several insurers. We show that a single budget-balanced allocation is implementable by an entry-proof tariff. In this allocation, different layers of coverage are fairly priced according to the types of consumers who purchase them, giving rise to cross-subsidies between types. This allocation can, under certain conditions, be uniquely implemented as the equilibrium outcome of a game as long as cross-subsidies between contracts are prohibited. In equilibrium, riskier consumers demand greater aggregate coverage at an increasing unit price, but the contracts offered by firms exhibit quantity discounts. We emphasize the need to regulate the supply side of insurance markets, while consumers can be left free to choose their preferred amount of coverage.