  We analyze a set of three PT-symmetric complex potentials, namely harmonic
oscillator, generalized Poschl-Teller and Scarf II, all of which reveal a
double series of energy levels along with the corresponding superpotential.
Inspired by the fact that two superpotentials reside naturally in order-two
parasupersymmetry (PSUSY) and second-derivative supersymmetry (SSUSY) schemes,
we complexify their frameworks to successfully account for the three
potentials.
