  Quantum-mechanical PT-symmetric theories associated with complex cubic
potentials such as V=x^2+y^2+igxy^2 and V=x^2+y^2+z^2+igxyz, where g is a real
parameter, are investigated. These theories appear to possess real, positive
spectra. Low-lying energy levels are calculated to very high order in
perturbation theory. The large-order behavior of the perturbation coefficients
is determined using multidimensional WKB tunneling techniques. This approach is
also applied to the complex Henon-Heiles potential V=x^2+y^2+ig(xy^2-x^3/3).
