  A new method for generating exactly solvable Schr\"odinger equations with a
position-dependent mass is proposed. It is based on a relation with some
deformed Schr\"odinger equations, which can be dealt with by using a
supersymmetric quantum mechanical approach combined with a deformed
shape-invariance condition. The solvability of the latter is shown to impose
the form of both the deformed superpotential and the position-dependent mass.
The conditions for the existence of bound states are determined. A lot of
examples are provided and the corresponding bound-state spectrum and
wavefunctions are reviewed.
