The adequateness of IIR models for acoustic echo cancellation is a long-standing question, and the answers found in the literature are conflicting. We use the results from rational Hankel norm and least-squares approximation, and we recall a test that provides a priori performance levels for FIR and IIR models. We apply this test to the measured acoustic impulse responses. Upon comparing the performance levels of FIR and IIR models with the same number of free parameters, we do not observe any significant gain from the use of IIR models. We attribute this phenomenon to the shape of the energy spectra of the acoustic impulse responses so tested, which possess many strong and sharp peaks. Faithful modeling of these peaks requires many parameters, irrespective of the type of the model.