Efficiency requirements often cause physical models of musical instruments to be vastly simplified when implemented, sometimes to the point where the model loses certain ``correct'' behaviors, such as realistic attacks or even stability. In the case of instability, many implementations which use fixed-point arithmetic implicitly rely on the limiting behavior of the number system to contain the amplitude of the signal. Certain models, such as clarinet models, tend to continue to work well in the presence of this instability, due to the fact that the resulting clipping does not significantly alter the spectral content of the signal. Other models, however, are significantly altered by the limiting. In certain cases, a simple nonlinear control system can be placed into the model (without significantly increasing the computation requirements) to serve the oscillation amplitude to a desired amplitude envelope. This control system improves the stability of the system, which in saturating number systems also reduces distortion. The control system can also improve other performance behaviors, such as attacks.