The Microcanonical Metropolis Monte Carlo (MMMC) method has been shown to describe reasonably well fragmentation of clusters composed of identical atomic species. However, this is not so clear in the case of heteronuclear clusters as some regions of phase space might be inaccessible due to the different mobility of the different atomic species, the existence of large isomerization barriers, or the quite different chemical nature of the possible intermediate species. In this paper, we introduce a constrained statistical model that extends the range of applicability of the MMMC method to such mixed clusters. The method is applied to describe fragmentation of isolated clusters with high, moderate, and no heteronuclear character, namely, CnHm, CnN, and Cn clusters for which experimental fragmentation branching ratios are available in the literature. We show that the constrained statistical model describes fairly well fragmentation of CnHm clusters in contrast with the poor description provided by the fully statistical model. The latter model, however, works pretty well for both Cn and CnN clusters, thus showing that the ultimate reason for this discrepancy is the inability of the MMMC method to selectively explore the whole phase space. This conclusion has driven us to predict the fragmentation patterns of the C4N cluster for which experiments are not yet available.