We discuss inversion of vertical-slice ocean-acoustic tomography (travel-time) measurements, in which we use the adiabatic-invariant approximation to convert multi-loop measurements to single-loop ray properties before using an Abel transform. We demonstrate the inversion by applying it to a simulated pulse-arrival sequence for a uniform sound channel generated by a ray tracing program, and compare the recovered sound-speed profile with that used for the simulation. For a uniform sound channel, the inversion gives both the symmetric and antisymmetric parts of the sound channel, including the vertical displacement of the sound-channel axis.