This paper investigates two approaches to patient classification: using patient classification only for sequencing patient appointments at the time of booking and using patient classification for both sequencing and appointment interval adjustment. In the latter approach, appointment intervals are adjusted to match the consultation time characteristics of different patient classes. Our simulation results indicate that new appointment systems that utilize interval adjustment for patient class are successful in improving doctors' idle time, doctors' overtime and patients' waiting times without any trade-offs. Best performing appointment systems are identified for different clinic environments characterized by walk-ins, no-shows, the percentage of new patients, and the ratio of the mean consultation time of new patients to the mean consultation time of return patients. As a result, practical guidelines are developed for managers who are responsible for designing appointment systems.