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This paper reverses the standard conclusion that asymmetric information plus competition results in insu cient insurance provision. Risk-tolerant individuals take few precautions and are disinclined to insure, but are drawn into a pooling equilibrium by the low premiums createdbythepresence of safer, more risk-averse types. Taxing insurance drives out the reckless clients, allowing a strict Pareto gain. This result depends on administrative costs in processing claims and issuing policies, as does the novel nding of a pure-strategy, partial-pooling, sub-game-perfect, Nash equilibrium in the insurance market. We would like to thank Heskey Bar-Issac, John Black, George Bulkley, Konstantinos Koufopoulos and especially the Editor Lars Stole and two referees for exceptionally helpful comments. Wewould also like to thank seminar participants at Universities of Bologna, Bocconi, Edinbugh, Exeter, Oxford, CEMFI, LSE and EARIE 2000 for useful discussions.

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