Given several systems’ automatic translations of the same sentence, we show how to combine them into a confusion network, whose various paths represent composite translations that could be considered in a subsequent rescoring step. We build our confusion networks using the method of Rosti et al. (2007), but, instead of forming alignments using the tercom script (Snover et al., 2006), we create alignments that minimize invWER (Leusch et al., 2003), a form of edit distance that permits properly nested block movements of substrings. Oracle experiments with Chinese newswire and weblog translations show that our confusion networks contain paths which are significantly better (in terms of BLEU and TER) than those in tercom-based confusion networks.