  In this paper we show that all 3-manifolds of a family introduced by M. J.
Dunwoody are cyclic coverings of lens spaces (eventually $\bf S^3$), branched
over genus one 1-bridge knots. As a consequence, we give a positive answer to
the Dunwoody conjecture that all the elements of a wide subclass are cyclic
coverings of $\bf S^3$ branched over a knot. Moreover, we show that all
branched cyclic coverings of a 2-bridge knot belong to this subclass; this
implies that the fundamental group of each branched cyclic covering of a
2-bridge knot admits a geometric cyclic presentation.
