Segmentation of range images has long been considered an important and difficult problem and continues to attract the attention of researchers in computer vision. In this paper we consider the problem of segmenting range images into planar regions. The approach we present combines different strategies for grouping image elements to estimate the parameters of the planes that best represent the range data. The strategies differ not only in the way candidate planes are hypothesized but also in the objective function used to select the best plane among the potential candidates. The main contribution of the paper is in an effective integration of simple modules. Experimental results on a large set of real range images are presented.