We prove that if X is a compact ANR homology n-manifold of dimension greater than 5, one can blow up the singularities of X to obtain the disjoint disks property. More precisely, X is the cell-like image of a compact ANR homology n-manifold with the disjoint disks property. We also prove a controlled analogue of the Bestvina-Walsh theorem on approximations of mappings by UV(k) mappings.