In fractal image compression a partitioning of the image is required. In this paper we discuss the construction of rate-distortion optimal partitions. We begin with a fine scale partition which gives a fractal encoding with a high bit rate and a low distortion. The partition is hierarchical, thus, corresponds to a tree. We employ a pruning strategy based on the generalized BFOS algorithm. It extracts subtrees corresponding to partitions and fractal encodings which are optimal in the rate-distortion sense. First results are included for the case of fractal encodings based on rectangular (HV) partitions. We also provide a comparison with greedy partitions based on the traditional collage error criterion or just using block variance.