The nature of the various types of wetting transitions for a given form of interaction potential is still somewhat controversial.14 In particular, the systematics of these transitions for inverse-power-law potentials is still an open In this Rapid Communication we investigate this problem for coarse-grained order-parameter interaction potentials of the general form w (r) - r(d+u) as rA‘Â 00, with u > 1 where d is the spatial dimension. After establishing the existence of stable mean-field (MF) profiles for u > 1 we determine the correct form of the effective Hamiltonian for I, the interface-substrate separation. It is then shown that there is a sequence of upper critical dimensions (UCD) in the problem and that for a given type of critical or multicritical transition three distinct types of behavior are possible, depending on the spatial dimension d. Denoting the jth UCD by dl, j0, 1, . . . , we show that for the potential V(l) given in (3b) below, a', is the spatial dimension where the operator l-(Â¥+j-l is marginal. In particular, for the critical wetting transition we find that (i) MF theory is correct for d > dl, l3 (ii) for dl > d > do fluctuations are strong enough to renormalize the exponents but there is no shift of the MF wetting temperature, and (iii) for do > d the wetting temperature is renormalized and all wetting transitions (including those described by MF theory to be first order) are continuous and belong to the same universality class. A similar sequencing occurs for all multicritical transitions. New results for the critical exponents in the intermediate dimension interval described in (ii) above are also derived and it is argued that for all d S 3, q, the anomalous dimension of the interface degree of freedom 1 is zero. Finally, these effects are illustrated by exact results for d = 2. The model we consider is described by the free-energy functional