The development of new, advanced engineering materials and the need for precise and flexible prototypes and low-volume production have made the wire electrical discharge machining (EDM) an important manufacturing process to meet such demands. This research investigates the effect of spark on-time duration and spark on-time ratio, two important EDM process parameters, on the material removal rate (MRR) and surface integrity of four types of advanced material: porous metal foams, metal bond diamond grinding wheels, sintered Nd-Fe-B magnets, and carbon-carbon bipolar plates. An experimental procedure was developed. During the wire EDM, five types of constraints on the MRR due to short circuit, wire breakage, machine slide speed limit, and spark on-time upper and lower limits are identified. An envelope of feasible EDM process parameters is generated for each work-material. Applications of such a process envelope to select process parameters for maximum MRR and for machining of micro features are discussed. Results of Scanning Electron Microscopy (SEM) analysis of surface integrity are presented.