Iterative solvers are required for the discrete-time simulation of nonlinear behaviour in analogue distortion circuits. Unfortunately, these methods are often computationally too expensive for realtime simulation. Two methods are presented which attempt to reduce the expense of iterative solvers. This is achieved by applying information that is derived from the specific form of the nonlinearity. The approach is first explained through the modelling of an asymmetrical diode clipper, and further exemplified by application to the Dallas Rangemaster Treble Booster guitar pedal, which provides an initial perspective of the performance on systems with multiple nonlinearities.