The application of general clock skew scheduling is practically limited due to the difficulties in implementing a wide spectrum of dedicated clock delays in a reliable manner. This results in a significant limitation of the optimization potential. As an alternative, the application of multiple clocking domains with dedicated phase shifts that are implemented by reliable, possibly expensive design structures can overcome these limitations and substantially increase the implementable optimization potential of clock adjustments. In this paper we present an algorithm for constrained clock skew scheduling which computes for a given number of clocking domains the optimal phase shifts for the domains and the assignment of the individual registers to the domains. For the withindomain latency values, the algorithm can assume a zero-skew clock delivery or apply a user-provided upper bound. Our experiments demonstrate that a constrained clock skew schedule using a few clocking domains combined...