First-break traveltimes can be accurately computed by the finite-difference solution of the eikonal equation using a new corner-node discretization scheme. It offers accuracy advantages over the traditional cell-centered node scheme. A substantial efficiency improvement is achieved by the incorporation of a wavefront tracking algorithm based on the construction of a minimum traveltime tree. For the traditional discretization scheme, an accurate average value for the local squared slowness is found to be crucial in stabilizing the numerical scheme for models with large slowness contrasts. An improved method based on the traditional discretization scheme can be used to calculate traveltimes in arbitrarily varying velocity models, but the method based on the corner-node discretization scheme provides a much better solution.