The relation between crime and police outlays is estimated using State observations for the 1970-1980 period. Empirical findings indicate that it is possible to reduce crime in the short-term by increasing police expenditures. In the long-term, however, criminals may adjust to the new level of police efforts and increase their criminal activities. This phenomenon is referred to as the ability of criminals to 'learn by doing' and may explain why, over the long-term, the level of crime is positively associated with police expenditures. That is, once criminals are acquainted with new police practices, they increase the number of crimes, returning to the crime level that existed before deterring activities were enhanced. It is concluded that real police expenditures need to increase over time in order to maintain crime below the 'natural' level. Over the long-term, the 'natural' crime rate may change as socioeconomic factors vary. 15 references, 3 tables, 2 figures.