In Mojalal et al (2019), the waiting time distribution for the lowest class in the Delayed Accumulating Priority Queue (APQ) is presented. In the Delayed APQ, lower priority class customers wait for fixed periods of time before accumulating priority, leading to longer waiting times over a regular APQ. We exploit a theorem in that paper to quantify the amount of reduction in the mean waiting time of class-1 customers over a regular APQ as a function of the value of the initial delay period d, in a 2-class Delayed APQ. We also quantify the corresponding increase for class-2 customers. Numerical examples will be presented.