We introduce a framework for reducing the number of element comparisons performed in priority-queue operations. In particular, we give a priority queue which guarantees the worst-case cost of O (1) per minimum finding and insertion, and the worst-case cost of O (log n ) with at most log n + O (1) element comparisons per deletion, improving the bound of 2 log n + O (1) known for binomial queues. Here, n denotes the number of elements stored in the data structure prior to the operation in question, and log n equals log 2 (max {2, n}). As an immediate application of the priority queue developed, we obtain a sorting algorithm that is optimally adaptive with respect to the inversion measure of disorder, and that sorts a sequence having n elements and I inversions with at most n log ( I / n ) + O ( n ) element comparisons.