We present a wavefront ray tracing (WRT) technique for computing multivalued arrivals in a smooth 3-D velocity model. We combine the advantages of the wavefront construction method and the classical ray shooting tech- nique. For an efficient estimation of output quantities (traveltime, slowness, geometrical spreading) from rays to gridpoints, we propagate a wavefront stepwise through the model. In case of insufficient ray illumination of the subsurface, we shoot new rays directly from the source point. This leads to accurate initial condition which is not possible by the interpolation of new rays on the wavefront. To increase the computational efficiency we only use kinematic ray tracing and liniar interpolation of model parameters (velocity and it's first derivatives).