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.