We introduce a new notion of classification accuracy based on the top τ -quantile values of a scoring function, a relevant criterion in a number of problems arising for search engines. We define an algorithm optimizing a convex surrogate of the corresponding loss, and show how its solution can be obtained by solving a set of convex optimization problems. We also present margin-based guarantees for this algorithm based on the top τ -quantile of the scores of the functions in the hypothesis set. Finally, we report the results of several experiments in the bipartite setting evaluating the performance of our algorithm and comparing the results to several other algorithms seeking high precision at the top. In most examples, our algorithm achieves a better performance in precision at the top.