  Dynamical systems exhibiting both PT and Supersymmetry are analyzed in a
general scenario. It is found that, in an appropriate parameter domain, the
ground state may or may not respect PT-symmetry. Interestingly, in the domain
where PT-symmetry is not respected, two superpotentials give rise to one
potential; whereas when the ground state respects PT, this correspondence is
unique. In both scenarios, supersymmetry and shape-invariance are intact,
through which one can obtain eigenfunctions and eigenstates exactly. Our
procedure enables one to generate a host of complex potentials which are not
PT-symmetric, and can be exactly solved.
