When drilling into a petroleum reservoir it is critical to maintain a required downhole pressure to avoid well bore fracture or influx of petroleum fluids. Drilling into mature and often depleted petroleum fields may be difficult due to tight pressure margins. This paper evaluates various automatic control designs for co-ordinating pump rates and choke valve during managed pressure drilling operations. The main focus is on evaluating a nonlinear model predictive controller based on a low-order model for automatic co-ordination of main mud pump, backpressure pump and topside choke opening to control the bottom hole pressure in the well. The nonlinear model predictive control designs are compared with a single input single output PI controller. In addition, the control designs are also combined with a downhole pressure observer. The various control designs are evaluated by computer simulation with a high-fidelity dynamic multi-phase flow model based on a North Sea off-shore drilling operation. The results show that introducing a nonlinear model predictive control design for co-ordinating the pump rates and choke valve both improves the downhole pressure control and also significantly simplifies the procedure for the drilling crew.