  We start with quasi-exactly solvable (QES) Hermitian (and hence real) as well
as complex PT-invariant, double sinh-Gordon potential and show that even after
adding perturbation terms, the resulting potentials, in both cases, are still
QES potentials. Further, by using anti-isospectral transformations, we obtain
Hermitian as well as PT-invariant complex QES periodic potentials. We study in
detail the various properties of the corresponding Bender-Dunne polynomials.
