Tuning numerical libraries has become more difficult over time, as systems get more sophisticated. In particular, modern multicore machines make the behaviour of algorithms hard to forecast and model. In this paper, we tackle the issue of tuning a dense QR factorization on multicore architectures using a fully empirical approach.We exhibit a few strong empirical properties that enable us to efficiently prune the search space. Our method is automatic, fast and reliable. The tuning process is indeed fully performed at install time in less than one hour and ten minutes on five out of seven platforms. We achieve an average performance varying from 97% to 100% of the optimum performance depending on the platform. This work is a basis for autotuning the PLASMA library and enabling easy performance portability across hardware systems.