We consider a model of a two-dimensional interface of the (continuous) SOS
type, with finite-range, strictly convex interactions. We prove that, under
an arbitrarily weak pinning potential, the interface is localized. We cons
ider the cases of both square well and delta potentials. Our results extend
and generalize previous results for the case of nearest neighbours Gaussia
n interactions in [7] and [1]. We also obtain the tail behaviour of the hei
ght distribution, which is not Gaussian.