  By a theorem of Banagl-Chriestenson, intersection spaces of depth one
pseudomanifolds exhibit generalized Poincar\'{e} duality of Betti numbers,
provided that certain characteristic classes of the link bundles vanish. In
this paper, we show that the middle-perversity intersection space of a depth
one Witt space can be completed to a rational Poincar\'{e} duality space by
means of a single cell attachment, provided that a certain rational Hurewicz
homomorphism associated to the link bundles is surjective. Our approach
continues previous work of Klimczak covering the case of isolated singularities
with simply connected links. For every singular stratum, we show that our
condition on the rational Hurewicz homomorphism implies that the
Banagl-Chriestenson characteristic classes of the link bundle vanish. Moreover,
using Sullivan minimal models, we show that the converse implication holds at
least in the case that twice the dimension of the singular stratum is bounded
by the dimension of the link. As an application, we compare the signature of
our rational Poincar\'{e} duality space to the Goresky-MacPherson intersection
homology signature of the given Witt space. We discuss our results for a class
of Witt spaces having circles as their singular strata.
