The rational buyer procedure provides the competitive procurement of capacity-based ancillary services (AS) in unbundled markets by the independent grid operator (IGO). The capacity-based AS are prioritized in order of ascending response times. Prioritization allows substitutability of the AS by automatically making the unused capacity of a higher priority AS usable for any lower priority ASwithout the need of submitting additional offers.We develop an efficient scheme for the rational buyer procedure for the acquisition of the prioritizable capacity-based AS. The scheme allows the simultaneous determination of the successful offers in the multiauction procedure through the effective deployment of discrete programming notions and the exploitation of the structural characteristics of the formulation. A key feature is the incorporation of physical constraints such as capacity, ramp-rate, and interzonal constraints. The use of bounding techniques combined with procedures for the quick detection of infeasible combinations of the offer prices and the identification of avoidable calculations leads to reducing the computational burden. The effectiveness and computational efficiency of the scheme are illustrated with representative numerical results including case studies based on the IEEE 118-bus network.