In the course of formulating detailed models of complex chemical reactions, it is sometimes the case that modifications intended to account for one set of experimental observations wind up destroying a model's ability to account for other results. Here, we consider a recently proposed model of the peroxidase-oxidase reaction which derives from an earlier scheme via the addition of NADH oxidation by superoxide anion or its protonated form, hydroperoxyl radical. This modification was introduced to account for the observation of bistability and bursting at enzyme concentrations less than 0.5 muM Left unanswered in our previous paper was the matter of whether the proposed "fix" invalidates previously published examples of model-data agreement at higher enzyme concentrations. In the present paper, we show that under these latter circumstances, the new mechanism is as good as, and in some instances superior to, its predecessor. More generally, we argue that the consequences of NADH oxidation by O-2(-) or HO2. should be manifest principally at low enzyme concentrations, thereby offering a "global" explanation of our findings, Neither our original model, nor the derivative scheme treated here, provides for reactions involving NAD dimers, a species in which there has recently been renewed interest. Most importantly, it has been proposed to replace the reduction of coIII (an enzyme intermediate) by NAD radicals, a reaction for which there is no direct evidence, with the corresponding reaction involving NAD(2). While a detailed assessment of the consequences of dimer chemistry to theoretical peroxidase-oxidase dynamics is beyond the scope of the present investigation, it is easily documented that this substitution, by itself, abolishes oscillatory behavior for all model parametrizations previously considered. Moreover, this result appears to obtain for arbitrarily small values of the associated rate constant. Whether or not the inclusion of additional dimer reactions can restore the model's ability to account for experimental observations of complex dynamics remains to be determined.