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 -symmetric Hamiltonians. The method is applied to the Hermitian analogue of the -symmetric cubic anharmonic oscillator. A new example is provided by a Hamiltonian (approximately) equivalent to a -symmetric extension of the one-parameter trigonometric Pöschl-Teller potential. © 2006 IOP Publishing Ltd.