  The superconductor-insulator transition in the presence of strong
compensation of dopants was recently realized in La doped YBCO. The
compensation of acceptors by donors makes it possible to change independently
the concentration of holes n and the total concentration of charged impurities
N. We propose a theory of the superconductor-insulator phase diagram in the
(N,n) plane. It exhibits interesting new features in the case of strong
coupling superconductivity, where Cooper pairs are compact, non-overlapping
bosons. For compact Cooper pairs the transition occurs at a significantly
higher density than in the case of spatially overlapping pairs. We establish
the superconductor-insulator phase diagram by studying how the potential of
randomly positioned charged impurities is screened by holes or by strongly
bound Cooper pairs, both in isotropic and layered superconductors. In the
resulting self-consistent potential the carriers are either delocalized or
localized, which corresponds to the superconducting or insulating phase,
respectively.
