Researchers are often interested in estimating the effect of sustained use of a treatment on a health outcome. However, adherence to strict treatment protocols can be challenging for individuals in practice and, when non-adherence is expected, estimates of the effect of sustained use may not be useful for decision making. As an alternative, more relaxed treatment protocols which allow for periods of time off treatment (i.e. grace periods) have been considered in pragmatic randomized trials and observational studies. In this article, we consider the interpretation, identification, and estimation of treatment strategies which include grace periods. We contrast natural grace period strategies which allow individuals the flexibility to take treatment as they would naturally do, with stochastic grace period strategies in which the investigator specifies the distribution of treatment utilization. We estimate the effect of initiation of a thiazide diuretic or an angiotensin-converting enzyme inhibitor in hypertensive individuals under various strategies which include grace periods.