  Let k be an algebraically closed field of characteristic 2, and let W be the
ring of infinite Witt vectors over k. Suppose G is a finite group and B is a
block of kG with a dihedral defect group D such that there are precisely two
isomorphism classes of simple B-modules. We determine the universal deformation
ring R(G,V) for every finitely generated kG-module V which belongs to B and
whose stable endomorphism ring is isomorphic to k. The description by Erdmann
of the quiver and relations of the basic algebra of B is usually only
determined up to a certain parameter c which is either 0 or 1. We show that
R(G,V) is isomorphic to a subquotient ring of WD for all V as above if and only
if c=0, giving an answer to a question raised by the first author and Chinburg
in this case. Moreover, we prove that c=0 if and only if B is Morita equivalent
to a principal block.
