We extend the analytical theory explaining the trapping of normally dispersive waves by a Raman soliton in an axially uniform optical fiber to include axially nonuniform fibers. It is shown how a changing group velocity in such a fiber leads to the same trapping mechanism as for a decelerating Raman soliton in a uniform fiber. In contrast to this latter case, where the trapping always leads to a blueshift of the confined radiation, the additional design flexibility inherent in the nonuniform geometry permits the redshift of dispersive waves trapped by an accelerating soliton, which itself may blueshift as a result of the associated spectral recoil.
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