  Recently Ritter and Weiss introduced an equivariant "main conjecture" than
generalizes and refines the Main Conjecture of Iwasawa theory. In this paper,
we show that, for the prime 2 and a dihedral extension of order 8 over Q, this
conjecture is equivalent to a congruence condition on the coefficients of a
power series with 2-adic integral coefficients constructed using the 2-adic
L-series associated to the extension. We then verify that this congruence
condition holds for the first coefficients in a large number of examples.
