Applying the fast marching method to solve the eikonal equation on the 3-D SEG/EAGE salt-dome model demonstrates two key features of the method, stability and efficiency. Such an application, also reveals some of the accuracy deficiencies of the Cartesian-coordinate implementation of the fast marching method. The accuracy is improved by applying the fast marching method in spherical coordinates. Obviously, this domain better represents waves emanating from a point source than the Cartesian coordinates. However, the finite-difference solution of the eikonal equation, in any domain, provides traveltimes corresponding only to the fastest arrivals. These arrivals, in inhomogeneous media, include typically head-waves and other low-energy waves. The eikonal solution of the salt-dome model includes a lot of low energy waves, such as head-waves emanating from the top of the salt structure. These low-energy waves have replaced the more important direct waves in many regions of the solution. Using such a traveltime solution for imaging will result in a less than ideal image.