Two techniques for computing ray synthetic seismograms in anelastic media produce substantially different results in a model consisting of an elastic half-space overlying a stack of anelastic layers (Krebes and Slawinski, 1991). The first technique, the stationary ray method, involves an evaluation of the wave field integral by the method of steepest descent, and yields complex rays. In the second, the conventional ray method, it is assumed that the attenuation vector of the initial ray segment (in the elastic part of the model) is zero (which is not the case for the stationary ray). The essential difference between these two methods is that the stationary ray method gives minimum travel-time rays, thus agreeing with Fermat's principle. Krebes and Slawinski (1991) relied upon this fact to suggest that the stationary ray method is the correct method. However, since the method raises some conceptual peculiarities (e.g., the initial ray segment of the stationary ray is an inhomogeneous elastic wave propagating as a body wave), it is important to verify their results and conclusions with an independent solution of the problem; we use a numerical finite-difference solution. By making direct comparisons between synthetic seismograms obtained with the stationary ray method, conventional ray method, and finite differences, we find that the stationary ray method agrees with the finite-difference solution better than the conventional ray method.