In atomic and molecular spectroscopy, measured transition energies represent differences between the energy levels of the emitting or absorbing system. In complex spectra of such transitions, the assignment of the pair of states corresponding to an observed transition energy is a difficult process. These assignments evolve in stages. At each stage, some assignments will be erroneous. Robust fitting methods have proven extremely helpful for finding gross errors and for obtaining reliable estimates of energy levels in the analysis of molecular tritium (T2) spectra. The robust results can be used successfully to obtain new assignments of transition energies to energy levels. In statistical terms, a highly unbalanced two-way analysis of variance model results. Some specific robustness problems that call for further research are mentioned. An iterative algorithm that is fast and avoids storage problems, even for large data sets, is described. This algorithm can be used for both least squares and robust fitting of incomplete two-way tables and similar designs.