We prove that a certain class of ALE spaces always has a Kahler conformal
compactification, and moreover provide explicit formulas for the conformal
factor and the Kahler potential of said compactification. We then apply this to
give a new and simple construction of the canonical Bochner-K\"ahler metric on
certain weighted projective spaces, and also to explicitly construct a family
Kahler edge-cone metrics on CP2, with singular set CP1,
having cone angles 2πβ for all β>0. We conclude by discussing how
these results can be used to obtain certain well-known Einstein metrics.Comment: 14 page