We consider the reduction of the intensity fluctuations in a laser by intracavity nonlinear absorption. The optimum operating conditions for reducing the intracavity intensity fluctuations are not the same as the conditions for reducing the intensity fluctuations in the output field. For a quite general class of models, we show that at the optimum operating point for reducing intensity fluctuations in the output field reduction in the intracavity intensity fluctuations is half of the maximum level that can be achieved in the model. We also show that as the laser intensity fluctuations are reduced the phase fluctuations, as measured by the laser linewidth, are correspondingly increased.