  Let G be an infinite cyclic extension, 1 -> B -> G -> Z -> 1, of a group B
where the action of Z on the set of conjugacy classes of non-trivial elements
of B is free. This class of groups includes certain ascending HNN-extensions
with abelian or free base groups, certain wreath products by Z and the soluble
Baumslag-Solitar groups BS(1,m) with |m|> 1. We construct a model for Evc(G),
the classifying space of G for the family of virtually cyclic subgroups of G,
and give bounds for the minimum dimension of Evc(G). We construct a
2-dimensional model for Evc(G) where G is a soluble Baumslag-Solitar BS(1,m)
group with |m|>1 and we show that this model for Evc(G) is of minimal
dimension.
