  We construct explicit examples of quaternion-K\"ahler and hypercomplex
structures on bundles over hyperK\"ahler manifolds. We study the infinitesimal
symmetries of these examples and the associated Galicki-Lawson
quaternion-K\"ahler moment map. By performing the QK reduction we produce
several explicit QK metrics. Moreover we are led to a new proof of a
hyperK\"ahler/quaternion-K\"ahler type correspondence. We also give examples of
other Einstein metrics and balanced Hermitian structures on these bundles.
