  The following comparison rules for the discrete spectrum of the
position-dependent mass (PDM) Schroedinger equation are established. (i) If a
constant mass $m_0$ and a PDM $m(x)$ are ordered everywhere, that is either
$m_0\leq m(x)$ or $m_0\geq m(x)$, then the corresponding eigenvalues of the
constant-mass Hamiltonian and of the PDM Hamiltonian with the same potential
and the BenDaniel-Duke ambiguity parameters are ordered. (ii) The corresponding
eigenvalues of PDM Hamiltonians with the different sets of ambiguity parameters
are ordered if $\nabla^2 (1/m(x))$ has a definite sign. We prove these
statements by using the Hellmann-Feynman theorem and offer examples of their
application.
