Cost-effectiveness analysis has become a widely accepted tool for decision making in health care. The standard textbook cost-effectiveness analysis focuses on whether to make the switch from an old or common practice technology to an innovative technology, and in doing so, it takes a global perspective. In this article, we are interested in a local perspective, and we look at the questions of whether and when the switch from old to new should be made. A new approach to cost-effectiveness from a local (e.g., a hospital) perspective, by means of a mathematical model for cost-effectiveness that explicitly incorporates time, is proposed. A decision rule is derived for establishing whether a new technology should be adopted, as well as a general rule for establishing when it pays to postpone adoption by 1 more period, and a set of decision rules that can be used to determine the optimal timing of adoption. Finally, a simple example is presented to illustrate our model and how it leads to optimal decision making in a number of cases.