The analysis considers optimal fines in a model in which individuals can commit up to two offenses. The fine for the second offense is allowed to differ from the fine for the first offense. When deciding whether to commit the first offense, individuals take into account the fine that may be imposed on them if they subsequently commit a second offense. Thus, a policy of increasing penalties achieves better deterrence because it indirectly imposes higher penalties on individuals with higher offense propensities. Other deterrence rationales for an increasing punishment policy are the need to make the level of punishment rise to make up for the declining probability of punishment of a more experienced offender and the need to impose higher penalties on repeat offenders to offset the declining deterrent effect of the stigma attached to the fact of being punished. Appended methodological information, list of other working papers, and 9 references