Several methods have recently been proposed for representing oscillatory wavefunctions by relatively slowly varying modulations of known oscillatory functions. Direct computation of the modulating function leads to efficient numerical or variational procedures and to accurate interpolation over energy or other parameters of a scattering problem. A new method, based on the phase integral (WKB) formalism, is proposed here in a form applicable to multichannel scattering. The method generalizes the phase integral method to make use of arbitrary oscillatory comparison functions, rather than just plane waves as in the usual formalism. It makes use of the modulating factor of the radial Jost function. Several examples of the proposed method are given, including an application to a two-channel model problem. Copyright © 1973 by the American Institute of Physics.