This paper addresses the linear spectral unmixing problem, by incorporating different constraints that may be of interest in order to cope with spectral variability: sparsity (few nonzero abundances), group exclusivity (at most one nonzero abundance within subgroups of endmembers) and significance (non-zero abundances must exceed a threshold). We show how such problems can be solved exactly with mixed-integer programming techniques. Numerical simulations show that solutions can be computed for problems of limited, yet realistic , complexity, with improved estimation performance over existing methods, but with higher computing time. Index Terms-sparse spectral unmixing, L0-norm optimization , structured sparsity, mixed-integer programming.