The first part of this investigation [J. Acoust. Soc. Am.76, 1201–1207 (1984)] derived a perturbation representation of the velocity potential for an axisymmetric, monochromatic sound beam in the form of a complex function. That result, which used Hankel transforms to describe the dependence on transverse position, lacked uniform validity in the corresponding wavenumber, as well as the distance from the transducer. Expressions for the state variables derived from the potential have the same behavior. The example of a planar wave is used to adapt the singular perturbation method of renormalization to the case where the potential is in complex form. The resulting technique is used to obtain a coordinate straining transformation that makes the state variables uniformly accurate. The expression for the pressure is similar to the King integral in linear theory, except that the integrand is a function of the strained coordinates. Comparison of the predicted waveform properties with experimental data [Gallego‐Juarez and Gaete‐Garreton, J. Acoust. Soc. Am.73, 761–765 (1983)] shows good correlation. Further evaluations disclose some new features of the distortion phenomena in both the time and frequency domains.