This paper studies appointment scheduling for a combination of routine patients who book well in advance and last-minute patients who call for an appointment later that same day. We determine when these same-day patients should be scheduled throughout the day, and how the prospect of their arrivals affects the appointment times of the routine patients. By formulating the problem as a stochastic linear program, we are able to incorporate random and heterogeneous service times and no-show rates, ancillary physician tasks, and appointment delay costs for same-day patients who prefer to see the doctor as early as possible. We find that the optimal patient sequence is quite sensitive to the no-show probabilities and the expected number of same-day patients. We also develop two simple heuristic solutions to this combinatorial sequencing problem.