We consider linear programming (LP) models for metabolic networks in which alternate optima often arise, and need to be identified to allow for data interpretation or the effective design of follow-up experiments. A recursive mixed-integer linear programming (MILP) algorithm is proposed for rigorously finding all alternate optima. The carbon trafficking alternatives of an Escherichia coil mutant lacking pyruvate kinase are analyzed with the proposed algorithm. The results are discussed in terms of using them as an input to isotopomer mapping matrix calculations in order to design C-13 NMR experiments for maximum contrast.