I present a new, general formal model of nuclear brinkmanship. The novelty here is that the threat of nuclear escalation comes about inadvertently, making it a function of conflict duration with a non-monotonic relationship to conventional capabilities. When two states have similar conventional capabilities and enter into a war, the conventional conflict will be prolonged, thus resulting in high degrees of nuclear risk. When two states have dissimilar conventional capabilities, conventional conflict will be one-sided and short, thus resulting in low degrees of nuclear risk. The model generates a series of results, including evidence of the nuclear peace, of conflict patterns consistent with the stability-instability paradox, and of the merits of ``burning bridges.’’ Additionally, the model generates mixed results on the feasibility of using catastrophic nuclear risk as a substitute for conventional arming.