We investigate complex PT-symmetric potentials, associated with quasi-exactly
solvable non-hermitian models involving polynomials and a class of rational
functions. We also look for special solutions of intertwining relations of SUSY
Quantum Mechanics providing a partnership between a real and a complex
PT-symmetric potential of the kind mentioned above. We investigate conditions
sufficient to ensure the reality of the full spectrum or, for the quasi-exactly
solvable systems, the reality of the energy of the finite number of levels.