We study road safety when insurance companies have market power, and can influence drivers' behavior via insurance premiums. We obtain first- and second-best premiums for different insurance market structures. The insurance program consists of an insurance premium, and marginal dependencies of that premium on speed and own safety technology choice of drivers. A private monopolist internalizes collision externalities up to the point where compensations to users' benefit matches the full (intangible) costs; in oligopolistic markets, insurers do not fully internalize collision externalities. Analytical results demonstrate how insurance firms' incentives to influence traffic safety coincide with or deviate from socially optimal incentives. Our results may be useful for design of pay-as-you-speed and alike insurances as well as policies related to driving safety.