A relation between the distribution of customer-servicing times and that of customer-waiting times is derived for the case of a single-channel queue with random arrivals and the rule of “first come, first served” establishing the order of service. The queue is assumed to be in a state of statistical equilibrium. The relation holds for a large class of the servicing-time distributions that occur in practice, in particular the cases of constant, exponential, and Type III Pearson servicing times. The derivation takes into account changes in the magnitude of demand from customer to customer, changes that may exist in many of the situations in which the theory is likely to be applied. Using the theory, the characteristics of the waiting-time distributions associated with several specific types of servicing-time distributions are discussed. It is shown that if it is possible to make the right sort of alterations in servicing-time distributions considerable reduction in customer waiting times can be made. The analytical results are illustrated with graphs. Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.