In this paper, the control of a physical model of a trumpet is studied. Although this model clearly describes the mechanical and acoustical phenomena that are perceptually relevant, additional constraints must be imposed on the control parameters. In contrast with the model where the tube length can be varied continuously, only seven different tube lengths can be obtained with a real instrument. By studying the physical model and its implementation, different relationships between the control parameters and signal characteristics are identified. These relationships are then used to obtain the best set of tube lengths with respect to a given tuning frequency.