  By considering the Bredon analogue of complete cohomology of a group, we show
that every group in the class $\LHFF$ of type Bredon-$\FP_\infty$ admits a
finite dimensional model for $\EFG$.
  We also show that abelian-by-infinite cyclic groups admit a $3$-dimensional
model for the classifying space for the family of virtually nilpotent
subgroups. This allows us to prove that for $\mF,$ the class of virtually
cyclic groups, the class of $\LHFF$-groups contains all locally virtually
soluble groups and all linear groups over $\mathbb C$ of integral
characteristic.
