The need for flexible service provision in electric power systems has dramatically increased due to the growing penetration of variable energy resources, as has the need to ensure fair access and compensation for this provision. A swing contract (SC) facilitates flexible service provision because it permits multiple service attributes to be offered together in bundled form with each attribute expressed as a range of possible values rather than as a single point value. This paper discusses a new SC Market Design for electric power systems that permits SCs to be offered by any dispatchable resource. An analytical optimization formulation is developed for the clearing of an SC day-ahead market that can be implemented using any standard mixed integer linear programming (MILP) solver. The practical feasibility of the optimization formulation is demonstrated by means of a numerical example.