Wells are commonly held at constant drawdown to maximize their discharge or to recover nonaqueous phase liquids, but only the simplest cases of constant drawdown wells have been treated analytically. In this paper the method of instantaneous source functions, which was originally limited to cases where the discharges of wells are specified, is extended to predict transient discharge and drawdown in the vicinity of wells held at constant drawdown. The analysis requires applying a Laplace transform to the Duhamel integral, rearranging the resulting algebraic expression, and then numerically inverting to obtain the discharge function that will result in a constant drawdown at a particular location. This approach allows flow problems with a wide range of geometries to be analyzed, and it also allows superposition to be used for transient problems without violating the condition of constant drawdown at the well. ¿ American Geophysical Union 1993