Ray perturbation theory is an efficient means of calculating raypaths and travel times in 3-D heterogeneous media accurate to first and second order respectively. We present results from using perturbation theory in 3-D quasi-random models of the earth's mantle and in a subduction model obtained from ISC tomography. We show that the perturbation theory provides travel time estimates with errors smaller than 0.1 s for a very wide range of heterogeneities. The second order travel time correction also removes the implicit bias, towards late arrivals, present in all first order estimates. The computational efficiency of the theory is discussed and actual cpu times are given. It is concluded that ray perturbation theory is both accurate and efficient enough to provide a basis for non-linear tomography on data sets with the order of a million rays. ¿American Geophysical Union 1993