A detailed analysis is carried out on both published experimental results and new experiments for the methylation kinetics of two site DNA substrates (with site separations between 100 and 800 bp) catalyzed by bacterial DNA adenine methyltransferase (Dam). A previously reported rate enhancement for the second methylation event (relative to that of the first methylation) is shown to result from elevated substrate specificity for singly methylated DNA over that of unmethylated DNA and not processive turnover of both sites by the same copy of Dam. An elementary model is suggested that cleanly fits the experimental data over a broad range of intersite separations. The model hypothesizes a looping mediated interference between competing unmethylated Dam sites on the same DNA strand.