The energy conservation equations due to Westervelt [Proc. 3rd. Int. Congr. Acoustics, edited by L. Cremer (Elsevier, Amsterdam, 1960), p. 316] are used to show that saturation effects in a finite amplitude wave can in principle be suppressed, if the attenuation coefficient at the second harmonic frequency of the primary wave can be selectively increased. Introduction of bubbles which are resonant at the second harmonic frequency is proposed as a scheme for practically implementing this idea. In the case of a parametric array, the parameter of nonlinearity also increases when the bubbles are introduced, thus, parametric efficiency can be enhanced while saturation is simultaneously suppressed.