||In this paper, we propose a new data-driven approach for binary descriptor selection. In order to draw a clear analysis of common designs, we present a general information-theoretic selection paradigm. It encompasses several standard binary descriptor construction schemes, including a recent state-of-the-art one named BOLD. We pursue the same endeavor to increase the stability of the produced descriptors with respect to rotations. To achieve this goal, we have designed a novel offline selection criterion which is better adapted to the online matching procedure. The effectiveness of our approach is demonstrated on two standard datasets, where our descriptor is compared to BOLD and to several classical descriptors. In particular, it emerges that our approach can reproduce equivalent if not better performance as BOLD while relying on twice shorter descriptors. Such an improvement can be influential for real-time applications.