Summary: Consider a single server exponential queueing system with \(N\) lines. After a service completion, the server chooses as its next customer the head of the line containing a special customer, with probability \(p\). Heads of other nonempty lines are chosen with equal probability. We study the distribution function of the waiting time of the special customer, under different combinations of jockeying for various values of \(p\). Potential applications are in health care and in airline communication systems. Computational results are given for a variety of model variants. Generalizations are discussed.