  For a knot K, the concordance crosscap number, c(K), is the minimum crosscap
number among all knots concordant to K. Building on work of G. Zhang, which
studied the determinants of knots with c(K) < 2, we apply the Alexander
polynomial to construct new algebraic obstructions to c(K) < 2. With the
exception of low crossing number knots previously known to have c(K) < 2, the
obstruction applies to all but four prime knots of 11 or fewer crossings.
