  We consider Hamiltonians associated with 3 dimensional conformally flat
spaces, possessing 2, 3 and 4 dimensional isometry algebras. We use the
conformal algebra to build additional {\em quadratic} first integrals, thus
constructing a large class of superintegrable systems and the complete Poisson
algebra of first integrals. We then use the isometries to reduce our systems to
2 degrees of freedom. For each isometry algebra we give a {\em universal}
reduction of the corresponding general Hamiltonian. The superintegrable
specialisations reduce, in this way, to systems of Darboux-Koenigs type, whose
integrals are reductions of those of the 3 dimensional system.
