Abstract: This paper examines the use of fines and imprisonment to deter individuals from engaging in harmful activities. These sanctions are analyzed separately as well as together, first for identical risk-neutral individuals and then for two groups of risk-neutral individuals who differ by wealth. When fines are used alone and individuals are identical, the optimal fine and probability of apprehension are such that there is some ‘underdeterrence’. If individuals differ by wealth, then the optimal fine for the high wealth group exceeds the fine for the low wealth group. When imprisonment is used alone and individuals are identical, the optimal imprisonment term and probability may be such that there is either underdeterrence or overdeterrence. If individuals differ by wealth, the optimal imprisonment term for the high wealth group may be longer or shorter than the term for the low wealth group. When fines and imprisonment are used together, it is desirable to use the fine to its maximum feasible extent before possibly supplementing it with an imprisonment term. The effects of risk aversion of these results are also discussed.