  We give, in dimensions three or greater, an example of a bounded,
pseudoconvex, circular domain in complex space with smooth real analytic
boundary and non-compact automorphism group which is not biholomorphically
equivalent to any Reinhardt domain. We give an analogous example in dimension
two, but the domain fails to be smooth at one boundary point---indeed it is not
in any Lipschitz class at the exceptional point.
