This paper investigates a two-class priority queue with decrementing service of a parameter (k1=, k2=k,1k) which operates as follows: Starting once a class-1 message service, a single server serves all messages in queue 1 until it becomes empty. After service completion in queue 1, the server switches over to queue 2 and continues serving messages in queue 2 until either queue 2 becomes empty, or the number of messages decreases to k less than that found upon the server's arrival at queue 2, whichever occurs first. It is assumed that arrival streams are Poissonian, message service times are generally distributed, and switch-over times are zero. We derive queue-length generating functions and LSTs of message waiting time distributions.