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Two-band analysis-synthesis filters or wavelet filters are used pervasively for compressing natural images. Both FIR and IIR filters have been studied in this context, the former being the most popular. In this paper, we examine the compression performance of these two-band filters in a dyadic wavelet decomposition and attempt to isolate features that contribute most directly to the performance gain. Then, employing the general exact reconstruction condition, hybrid FIR-IIR analysis-synthesis filters are designed to maximize compression performance for natural images. Experimental results are presented that compare performance with the popular biorthogonal filters in terms of peak SNR, subjective quality, and computational complexity .