We discuss how protein structure prediction schemes may be refined via a cumulant expansion approach using optimization criteria motivated by energy landscape ideas. The approach is advantageously combined with a free energy profile analysis based on multiple histogram sampling methods, which enables a quantitative assessment of the effects of refinement on the energy landscape to be made. The approach is widely applicable, but is illustrated here for a previously described prediction scheme intended for use in the absence of any known homology information. The relationship to previous optimization schemes is discussed.