  Recently an explicit resolution of the Calabi-Yau cone over the inhomogeneous
five-dimensional Einstein-Sasaki space Y^{2,1} was obtained. It was constructed
by specialising the parameters in the BPS limit of recently-discovered
Kerr-NUT-AdS metrics in higher dimensions. We study the occurrence of such
non-singular resolutions of Calabi-Yau cones in a more general context.
Although no further six-dimensional examples arise as resolutions of cones over
the L^{pqr} Einstein-Sasaki spaces, we find general classes of non-singular
cohomogeneity-2 resolutions of higher-dimensional Einstein-Sasaki spaces. The
topologies of the resolved spaces are of the form of an R^2 bundle over a base
manifold that is itself an $S^2$ bundle over an Einstein-Kahler manifold.
