This paper studies the effect of two service-level measures on the design of a critical-level policy for fast-moving items, where rationing is used to provide differentiated service levels to two classes of demand - high priority and low priority. Using the threshold-clearing mechanism under a strictly increasing non-negative demand to allocate backorders when multiple outstanding orders exist, we formulate service-level problems under type-I, fill-rate, and mixed service-level constraints to determine the optimal parameters of a continuous review (Q, r) policy with constant threshold value C to rationing the low-priority class. Based on several monotone properties, we proposed global search algorithms to solve the service-level problems, which guarantee reaching the globally optimal solution for any desired level of accuracy. Further results and a computational study demonstrate how these different models fare against each other in practice. (C) 2019 Elsevier Ltd. All rights reserved.