Computational discovery of cis-regulatory elements remains challenging. To cope with the high false positives, evolutionary conservation is routinely used. However, conservation is only one of the attributes of cis-regulatory elements and is neither necessary nor sufficient. Here, we assess two additional attributes--positional and inter-motif distance specificity--that are critical for interactions between transcription factors. We first show that for a greater than expected fraction of known motifs, the genes that contain the motifs in their promoters in a position-specific or distance-specific manner are related, both in function and/or in expression pattern. We then use the position and distance specificity to discover novel motifs. Our work highlights the importance of distance and position specificity, in addition to the evolutionary conservation, in discovering cis-regulatory motifs.