In this paper we determine the wetting phase diagram for three-dimensional systems with short-range forces assuming the presence of a position-dependent stiffness contribution as recently proposed [M.E. Fisher and A.J. Jin, Phys. Rev. Lett. 69, 792 (1992)]. We predict a discontinuous transformation of the phase diagram immediately upon moving beyond the mean-field approximation. However, in contrast to Fisher and Jin we find that a renormalization group calculation yields fluctuation-induced second-order transitions rather than fluctuation-induced first-order ones. As a consequence, in all fluctuation regimes we recover the same qualitative phase diagram as predicted in the absence of a position-dependent stiffness coefficient. Furthermore, recent predictions for tricritical wetting behavior remain unaffected by the stiffness contribution. © 2002 The American Physical Society.