We point out a simple construction of an infinite class of Einstein
near-horizon geometries in all odd dimensions greater than five. Cross-sections
of the horizons are inhomogeneous Sasakian metrics (but not Einstein) on
S^3xS^2 and more generally on Lens space bundles over any compact positive
Kaehler-Einstein manifold. They are all consistent with the known topology and
symmetry constraints for asymptotically flat or globally AdS black holes.