Summary: New algorithms for the classical problem of fairing cubic spline curves and bicubic spline surfaces are presented. To fair a cubic spline curve or a bicubic spline surface with abnormal portions, the algorithms (automatically or interactively) identify the ‘bad’ data points and replace them with new points produced by minimizing the strain energy of the new curve or surface. The proposed algorithms are more general than the existing algorithms in that the new algorithms can adjust more than one ‘bad’ data point in each modification step and they include the existing algorithms [J. F. Poliakoff, Comput.-Aided Des, 28, No. 1, 59–66 (1996; Zbl 0844.65005)] as special cases. Test results of the new algorithms are included.