  Extending the supersymmetric method proposed by Tkachuk to the complex
domain, we obtain general expressions for superpotentials allowing generation
of quasi-exactly solvable PT-symmetric potentials with two known real
eigenvalues (the ground state and first-excited state energies). We construct
examples, namely those of complexified non-polynomial oscillators and of a
complexified hyperbolic potential, to demonstrate how our scheme works in
practice. For the former we provide a connection with the sl(2) method,
illustrating the comparative advantages of the supersymmetric one.
