Subband coding is a powerful means for highly efficient image signal compression. We have proposed the optimum frequency band partition (OFBP) to improve the compression performance of subband image coding. OFBP determines an adaptive partition pattern on the 2-dimensional frequency domain considering the characteristics of an input image under the condition of a small number of subbands. However, the OFBP cannot obtain the optimum partition pattern in terms of rate-distortion sense for image compression. This is caused by the partition pattern being fixed, even if the desired bit rate changes. This paper presents an optimum space-frequency partition (OSFP) as a new OFBP. The optimized factors include the band partition on the 2-dimentional frequency domain, the combination of quantizers within subbands and the pruning of coefficient nodes in each subband (also referred to as the spatial domain partition), are optimized in terms of rate-distortion sense in case of an arbitrary given bit rate budget. Experimental results show the outperformance of several conventional image compression methods by the proposed OSFP coder.