  We construct new complete, compact, inhomogeneous Einstein metrics on S^{m+2}
sphere bundles over 2n-dimensional Einstein-Kahler spaces K_{2n}, for all n \ge
1 and all m \ge 1. We also obtain complete, compact, inhomogeneous Einstein
metrics on warped products of S^m with S^2 bundles over K_{2n}, for m>1.
Additionally, we construct new complete, non-compact Ricci-flat metrics with
topologies S^m times R^2 bundles over K_{2n} that generalise the
higher-dimensional Taub-BOLT metrics, and with topologies S^m \times R^{2n+2}
that generalise the higher-dimensional Taub-NUT metrics, again for m>1.
