The transcription start site (TSS) has been located for an increasing number of genes across several organisms. Statistical tests have shown that some cis-acting regulatory elements have positional preferences with respect to the TSS, but few strategies have emerged for locating elements by their positional preferences. This paper elaborates such a strategy. First, we align promoter regions without gaps, anchoring the alignment on each promoters TSS. Second, we apply a novel word-specific mask. Third, we apply a clustering test related to gapless BLAST statistics. The test examines whether any specific word is placed unusually consistently with respect to the TSS. Finally, our program A-GLAM, an extension of the GLAM program, uses significant word positions as new anchors to realign the sequences. A Gibbs sampling algorithm then locates putative cis-acting regulatory elements. Usually, Gibbs sampling requires a preliminary masking step, to avoid convergence onto a dominant but uninteresting signal from a DNA repeat. However, since the positional anchors focus A-GLAM on the motif of interest, masking DNA repeats during Gibbs sampling becomes unnecessary.