Ray theory is used to study the refraction of short oceanic internal waves by a spectrum of large amplitude inertia waves superimposed on a weakly sheared steady current. The results suggest that the steady current has a significant cumulative effect on short-wave propagation over the timescale of a few inertia periods. The strength of ray convergence is also computed, as this affects short-wave amplitudes. Typically we find weak ray convergence and much slower growth toward instability with increasing vertical wavenumber than in a steady-shear critical-layer model. ¿ 1999 American Geophysical Union