  The four-dimensional Kerr-de Sitter and Kerr-AdS black hole metrics have
cohomogeneity 2, and they admit a generalisation in which an additional
parameter characterising a NUT charge is included. In this paper, we study the
higher-dimensional Kerr-AdS metrics, specialised to cohomogeneity 2 by
appropriate restrictions on their rotation parameters, and we show how they too
admit a generalisation in which an additional NUT-type parameter is introduced.
We discuss also the supersymmetric limits of the new metrics. If one performs a
Wick rotation to Euclidean spacetime signature, these yield new Einstein-Sasaki
metrics in odd dimensions, and Ricci-flat metrics in even dimensions. We also
study the five-dimensional Kerr-AdS black holes in detail. Although in this
particular case the NUT parameter is trivial, our investigation reveals the
remarkable feature that a five-dimensional Kerr-AdS ``over-rotating'' metric is
equivalent, after performing a coordinate transformation, to an under-rotating
Kerr-AdS metric.
