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Summary Nowadays airborne laser scanning is used in many territorial studies, providing point data which may contain strong discontinuities. Motivated by the need to interpolate such data and preserve their edges, this paper considers robust nonparametric smoothers. These estimators, when implemented with bounded loss functions, have suitable jump-preserving properties. Iterative algorithms are developed here, and are equivalent to nonlinear M-smoothers, but have the advantage of resembling the linear Kernel regression. The selection of their coefficients is carried out by combining cross-validation and robust-tuning techniques. Two real case studies and a simulation experiment confirm the validity of the method; in particular, the performance in building recognition is excellent.