Starting by using the correct verbage can make that difference:
Saying things like "The doctor has set aside specific appointment times for your treatment" and then giving 2-3 different options for them to choose from. This gives the patient some control over choosing which time works for them and also meets your schedule goals.
Or if a patient want's to get in sooner than what you have available "The next appointment available is _____, lets go ahead and schedule you for that time and I will put you on an ASAP list. That way if an appointment comes available sooner, we will give you."
These are just a couple of examples of how you can control your schedule, make your patients happy and reduce stress!