The input data for refraction traveltime tomography are the traveltimes of the first breaks, which are picked using automatic pickers. Although automatic pickers perform satisfactorily overall, no one automatic picker can be characterized as the best one; one picker might fail for traces for which other pickers are accurate and vice versa for other traces. We introduce an iterative method for traveltime tomography, which takes as input traveltimes from a number of pickers. During the inversion scheme inconsistent traveltimes are replaced with more meaningful ones to obtain a smooth near-surface velocity model. The scheme is easily parallelizable and a byproduct of the inversion scheme is a set of consistent traveltimes which is close to the actual traveltimes of the first breaks.