Most insurance premiums are only weakly linked to mileage, and have largely lump-sum characteristics. The probable result is too many accidents and too much driving from the standpoint of economic efficiency. This paper develops a model of the relationship between driving and accidents that formalizes Vickrey's [1968] central insights about the accident externalities of driving. We use it to estimate the driving, accident, and congestion reduc- tions that could be expected from switching to other insurance pricing systems. Under a competitive system of per-mile premiums, in which insurance companies quote risk-classified per-mile rates, we estimate that the reduction in insured accident costs net of lost driving benefits would be $9.8 -$12.7 billion in the U.S., or $58-$75 per insured vehicle. When congestion reductions are considered, the net benefits rise to $15-$18 billion, exclusive of monitoring costs. The total benefits of per-mile premiums with a Pigouvian tax to account for accident externalities would be $19-$25 billion, or $111-$146 per insured vehicle, ex- clusive of monitoring costs. Accident externalities may go a long way toward explaining why most insurance companies have not switched to per-mile premiums despite these large potential social benefits.