The systematics of the wetting transition at solid-gas interfaces in systems interacting with inversepower-law potentials is investigated. The correct form of the effective Hamiltonian for l, the interfacesubstrate separation, is determined, and it is shown that for a given type of continuous wetting transition (e.g., critical wetting) there are three regimes of critical behavior, depending on the spatial dimension d. New results for the critical exponents in the intermediate regime are also presented.