  We formulate a systematic algorithm for constructing a whole class of
Hermitian position-dependent-mass Hamiltonians which, to lowest order of
perturbation theory, allow a description in terms of PT-symmetric Hamiltonians.
The method is applied to the Hermitian analogue of the PT-symmetric cubic
anharmonic oscillator. A new example is provided by a Hamiltonian
(approximately) equivalent to a PT-symmetric extension of the one-parameter
trigonometric Poschl-Teller potential.
