In this paper, we present two approaches which increase the efficiency of 3-D wavefront construction (WFC) methods. (WFC methods permit the computation of multivalued traveltimes for Kirchhoffmigration.) First, for the estimation of traveltimes within cells, we propose a distance-weighted averaging of extrapolated traveltimes. The extrapolation of traveltimes is performed under consideration of the wavefront curvature. Second, we introduce an insertion criterion for new rays. This criterion uses the difference in wavefront curvature between adjacent rays.