Measurements serve as the intermediate communication layer between the quantum world and our classical perception. So, the question which measurements efficiently extract information from quantum systems is of central interest... Using quantum steering as a nonclassical phenomenon, we show that there are instances, where the results of all two-outcome measurements can be explained in a classical manner, while the results of some three-outcome measurements cannot. This points at the important role of the number of outcomes in revealing the nonclassicality hidden in a quantum system. Moreover, our methods allow to improve the understanding of quantum correlations by delivering novel criteria for quantum steering and improved ways to construct local hidden variable models. (read more)