  Let Z be a finite set of double points in P^1 x P^1 and suppose further that
X, the support of Z, is arithmetically Cohen-Macaulay (ACM). We present an
algorithm, which depends only upon a combinatorial description of X, for the
bigraded Betti numbers of I_Z, the defining ideal of Z. We then relate the
total Betti numbers of I_Z to the shifts in the graded resolution, thus
answering a special case of a question of T. Roemer.
