The finite-difference traveltime algorithm presented by Van Trier and Symes (1989; 1990) uses a first-order upwind finite-difference scheme described by Engquist and Osher (1980). The Engquist-Osher scheme has an underlying physical minimization condition important for maintaining the stability of the algorithm; it also introduces approximations in the estimation of the traveltime field in order to obtain greater computational speed at the expense of accuracy. The error can be reduced in a slower algorithm. I extend the algorithm in 3-D and show results for a constant velocity medium and slowly varying velocity medium. I find there are greater stability problems in 3-D than in 2-D for rapidly varying velocity models.