We investigate how the transverse localization of light in evanescently coupled, disordered, lossless waveguide lattices depends on the shape and size of an input beam. Our detailed numerical study not only reveals waveguide-like propagation of the localized state inside such a disordered discrete medium but also shows that a specific localized state is independent of the spatial profile of the input beam. Dependence of the localized state on input beam parameters and lattice parameters is also reported. Our results should be of interest for engineering light propagation with discrete diffractive optics in practical optical geometries (e.g., microstructured arrays of optical waveguides, fiber arrays, etc.) and for realizing waveguide-like (without any diffractive spread) propagation even in the presence of structural disorders and refractive index perturbations. © 2010 Elsevier B.V. All rights reserved.