Spectral unmixing is an important technique for remotely sensed hyperspectral data exploitation. When hyperspectral unmixing relies on the use of spectral libraries (dictionaries of pure spectra), the sparse regression problem to be solved is severely ill-conditioned and time-consuming. This is due, on the one hand, to the presence of very similar signatures in the library and, on the other, to the existence in the library of spectral signatures that do not contribute to the observed mixtures. In practice, spectral libraries are highly coherent, which adds yet another complication. In this regard, the identification of a subset of signatures from the library which truly contribute to the observed mixtures has the potential to improve the conditioning of the problem and to considerably decrease the running time of the sparse unmixing algorithm. This paper proposes a methodology for obtaining such a dictionary pruning. The efficiency of the method is assessed using both simulated and real hyperspectral data.