In recent times quantum corrections for N = 2 black holes in 4 dimensi
ons have been addressed in the framework of double extreme black hole
solutions, which are characterised by constant scalar fields. In this
paper we generalize these solutions to non-constant scalar fields. Thi
s enables us to discuss quantum corrections for massless black holes a
nd for configurations that are classically singular. We also discuss t
he relation to the 5-dimensional magnetic string solution. (C) 1997 El
sevier Science B.V.