This paper explores revenue optimisation in a queueing system with two observable parallel queues, Poisson arrivals and rational customers. Customers pay a predetermined fee which depends on the queue they wish to join. This fee is a parameter that the provider can set to her liking. While a higher fee leads to more profit per customer, it also incentivises customers to opt for the less costly queue. We consider both a scenario in which customers always select a queue and one in which customers are allowed to balk. In the former case, a power series approximation method is accelerated by Wynn’s epsilon method. In the latter case, the queueing system constitutes a finite quasi-birth-death-type Markov chain and we rely on matrix-analytic techniques.