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We introduce a framework for reducing the number of comparisons performed in the deletion and minimum deletion operations for priority queues. In particular, we give a priority queue with constant cost per insertion and minimum finding, and logarithmic cost with at most logn+O(loglogn) comparisons per deletion and minimum deletion, improving over the bound of 2 logn+O(1) comparisons for the binomial queues and the pairing heaps. We also give a priority queue that supports, in addition to the above operations, the decrease-key operation. This latter priority queue achieves, in the amortized sense, constant cost per insertion, minimum finding and decrease-key operations, and logarithmic cost with at most 1.44logn+O(loglogn) comparisons per deletion and minimum deletion.