In previous work, we devised an approach for multilabel classification based on an ensemble of Bayesian networks. It was characterized by an efficient structural learning and by high accuracy. Its shortcoming was the high computational complexity of the MAP inference, necessary to identify the most probable joint configuration of all classes. In this work, we switch from the ensemble approach to the single model approach. This allows important computational savings. The reduction of inference times is exponential in the difference between the treewidth of the single model and the number of classes. We adopt moreover a more sophisticated approach for the structural learning of the class subgraph. The proposed single models outperforms alternative approaches for multilabel classification such as binary relevance and ensemble of classifier chains.