A search for low energy structures of water clusters was performed with a combination of three computational tools: (a) temperature-dependent classical trajectories; (b) hydrogen network improvement; (c) rigid body diffusion Monte Carlo calculation on a smoothed potential energy surface. For the sizes of our main interest, n = 48, 123, and 293, input configurations included spheroid structures cut from crystalline ice, and amorphous structures. For n = 48, tube and sandwich minima were explored as well. The lowest energy configurations found were characterized by compact three-dimensional shapes. In the case of n = 48 and 123, crystallinity was lost in the course of the optimization; for these sizes, one finds four-, five-, and six-membered rings of water molecules, On the other hand, the lowest energy structure found for n = 293 includes a crystal core, dominated by six-membered rings, and an amorphous surface.