Challenging multiclass classification problems such as image annotation may involve a large number of classes. In this context, confusion between classes may occur, and single label classification may be misleading. We provide in the present paper a general device that, given a classification procedure and an unlabeled dataset, outputs a set of class labels, instead of a single one. Interestingly, this procedure does not require that the unlabeled dataset explores the whole classes. Even more, the method is calibrated to control the expected size of the output set while minimizing the classification risk. We show the statistical optimality of the procedure and establish rates of convergence under the Tsybakov margin condition. It turns out that these rates are linear on the number of labels. We illustrate the numerical performance of the procedure on simulated and on real data. In particular, we show that with moderate expected size, w.r.t. the number of labels, the procedure provides significant improvement of the classification risk.