Two conflicting definitions of desistance exist in the criminology literature. The first definition is instantaneous desistance in which an offender simply chooses to end a criminal career instantaneously moving to a zero rate of offending (Blumstein et al., 1986). The second definition views desistance as a process by which the offending rate declines steadily over time to zero or to a point close to zero (Bushway et al., 2001; Laub and Sampson, 2001; Leblanc and Loeber, 1998). This article capitalizes on the underlying assumptions of several parametric survival distributions to gain a better understanding of which of these models best describes actual patterns of desistance. All models are examined using 18 years of follow-up data on a cohort of felony convicts in Essex County, NJ. The authors analysis leads them to three conclusions. First, some people have already desisted at the beginning of the follow-up period, which is consistent with the notion of "instantaneous desistance." Second, a three-parameter model that allows for a turning point in the risk of recidivism followed by a long period of decline fits the data best. This conclusion suggests that for those offenders active at the start of the study period, the risk of recidivism is declining over time. However, the authors also find that a simpler two-group model fits the data almost as well and gains superiority in the later years of follow-up. This last point is particularly relevant as it suggests that the observed gradual decline in the hazard over time is a result of a compositional effect rather than of a pattern of individually declining hazards. (Published Abstract)