Presentation of some new results showing how, under very general conditions, the recursive saddle-point method, pioneered by Marcet and Marimon, delivers the appropriate solution for contracting problems with intertemporal incentive constraints, with or without unique solutions. These results summarize work from: Marimon and Marcet "Recursive Contracts" (2011) and Marimon, Messner and Pavoni "Solving Recursive Contracts with Non-unique Solutions" (2011), as well as from ongoing work with Jan Werner: "On the Envelope Theorem without Differentiability" (2010).