  It is known that nilpotent orbits in a complex simple Lie algebra admit
hyperK\"ahler metrics with a single function that is a global potential for
each of the K\"ahler structures (a hyperK\"ahler potential). In an earlier
paper the authors showed that nilpotent orbits in classical Lie algebras can be
constructed as finite-dimensional hyperK\"ahler quotient of a flat vector
space. This paper uses that quotient construction to compute hyperK\"ahler
potentials explicitly for orbits of elements with small Jordan blocks. It is
seen that the K\"ahler potentials of Biquard and Gauduchon for SL(n)-orbits of
elements with X^2=0, are in fact hyperK\"ahler potentials.
