In many modern water networks, an emerging trend is to measure pressure at various points in the network for operational reasons. Because leaks typically induce a signature on pressure, these routine measurements can be used to develop nonintrusive leak detection approaches. This research employs successive linear approximation methods, based on linear programming and mixed integer linear programming, in a simulation-optimization framework to explore an alternative leak detection methodology for urban water distribution networks based on pressure measurements. The methods attempt to minimize the absolute differences between observed and simulated pressure values at the sensors to determine a linear combination of leaks that most closely approximates the observed pressure pattern. Steady-state and time-varying models of differing complexity (from small published networks to a 27,000-node network for a U.S. utility) were used to test the method. Results are presented to illustrate the method’s effectiveness under different conditions. The methods are shown to work well when pervasive pressure data and hydraulic models representing true operational conditions are available. The methods developed in this work are not intended to replace traditional leak detection methods; rather, they are meant to work in concert with available methods to more accurately and efficiently isolate leak locations and reduce water loss.