We consider the spectral stability of certain traveling wave solutions for the Boussinesq "abc" system. More precisely, we consider the explicit sech2(x) like solutions of the form ((x - wt),?(x - wt) = ( const.), exhibited by M. Chen [Appl. Math. Lett., 11 (1998), pp. 45-49], [Internat. J. Theoret. Phys., 37, (1998), pp. 1547-1567], and we provide a complete rigorous characterization of the spectral stability in all cases for which a = c < 0, b > 0. © 2013 Society for Industrial and Applied Mathematics.