Research on desistance in criminal involvement has focused on discovering if processes that lead to the onset and frequency of criminality are similar to the processes that lead to desistance. However, there is a lack of consensus on the meaning of “desistance” mainly caused by problems with measuring a lack of offending. In order to contribute to the understanding of desistance in criminal activities, the authors applied several different models, including the standard behavioral model, to estimate the proportion of the population who offended at least once before the age of 18 and who could be described as “desisters” by the age of 27. Data were drawn from the criminal history records of the 13,160 men in the 1958 Philadelphia Birth Cohort Study. Several different analytical frameworks are reviewed that represent differing meanings of desistance, which are identified as falling within three categories: (1) strict behavioral desistance, in which individuals do not engage in criminal activities during the follow-up period; (2) approximate desistance, in which individual engagement in criminal activities falls to a low level; and (3) split-population desistance, in which the uncertainty associated with studying criminal termination during a finite study period is taken into account. Results of the desistance study using the 1958 Philadelphia Birth Cohort Study are presented from the perspective of each of these three analytical frameworks. The strict behavioral desistance framework produced a desistance rate in the birth cohort sample of 61.2 percent. The approximate criminal desistance model estimated the probability of desistance for this population at 0.472, which was considerably lower than the estimate obtained from the strict behavioral model. Finally, the split-population model estimated that between 36.6 percent and 38.3 percent of the sample were “desisters.” The variability of these results illustrates that models and their assumptions matter significantly for social research. Finally, the authors contend that the split-population model offers the possibility of identifying true criminal “desisters.” Figures, tables, references