In (Wainwright et al., 2002) a new general class of upper bounds on the log partition function of arbitrary undirected graphical models has been developed. This bound is constructed by taking convex combinations of tractable distributions. The experimental results published so far concentrates on combinations of tree-structured distributions leading to a convexified Bethe free energy, which is minimized by the tree-reweighted belief propagation algorithm. One of the favorable properties of this class of approximations is that increasing the complexity of the approximation is guaranteed to increase the precision. The lack of this guarantee is notorious in standard generalized belief propagation. We increase the complexity of the approximating distributions by taking combinations of junction trees, leading to a convexified Kikuchi free energy, which is minimized by reweighted generalized belief propagation. Experimental results for Ising grids as well as for fully connected Ising models are presented illustrating advantages and disadvantages of the reweighting method in approximate inference.