  We use the quaternion Kahler reduction technique to study old and new
self-dual Einstein metrics of negative scalar curvature with at least a
two-dimensional isometry group, and relate the quotient construction to the
hyperbolic eigenfunction Ansatz. We focus in particular on the
(semi-)quaternion Kahler quotients of (semi-)quaternion Kahler hyperboloids,
analysing the completeness and topology, and relating them to the self-dual
Einstein Hermitian metrics of Apostolov-Gauduchon and Bryant.
