  Let $k$ be an algebraically closed field of characteristic 2, and let $W$ be
the ring of infinite Witt vectors over $k$. Suppose $D$ is a dihedral 2-group.
We prove that the universal deformation ring $R(D,V)$ of an endo-trivial
$kD$-module $V$ is always isomorphic to $W[\mathbb{Z}/2\times\mathbb{Z}/2]$. As
a consequence we obtain a similar result for modules $V$ with stable
endomorphism ring $k$ belonging to an arbitrary nilpotent block with defect
group $D$. This confirms for such $V$ conjectures on the ring structure of the
universal deformation ring of $V$ which had previously been shown for $V$
belonging to cyclic blocks or to blocks with Klein four defect groups.
