Background: Policies assigning low-priority patients treatment delays for care, in order to make room for patients of higher priority arriving later, are common in secondary healthcare services today. Alternatively, each new patient could be granted the first available appointment. We aimed to investigate whether prioritisation can be part of the reason why waiting times for care are often long, and to describe how departments can improve their waiting situation by changing away from prioritisation. Methods: We used patient flow data from 2015 at the Department of Otorhinolaryngology, Haukeland University Hospital, Norway. In Dynaplan Smia, Dynaplan AS, dynamic simulations were used to compare how waiting time, size and shape of the waiting list, and capacity utilisation developed with and without prioritisation. Simulations were started from the actual waiting list at the beginning of 2015, and from an empty waiting list (simulating a new department with no initial patient backlog). Results: From an empty waiting list and with capacity equal to demand, waiting times were built 7 times longer when prioritising than when not. Prioritisation also led to poor resource utilisation and short-lived effects of extra capacity. Departments where prioritisation is causing long waits can improve their situation by temporarily bringing capacity above demand and introducing "first come, first served" instead of prioritisation. Conclusion: A poor appointment allocation policy can build long waiting times, even when capacity is sufficient to meet demand. By bringing waiting times down and going away from prioritisation, the waiting list size and average waiting times at the studied department could be maintained almost 90% below the current level – without requiring permanent change in the capacity/demand ratio.