  By exploiting the role of the horizontal symmetry SL(2,R), we extend the
analysis and classification of two-centered extremal black hole charge
configurations to the case of "small" single-centered constituents. These
latter are seen to decrease the number of independent horizontal-invariant
polynomials from four to one, depending on the rank of the charge orbit
supporting each of the two centers. Within U-duality groups of type E7, both
reducible and irreducible symmetric supergravity models in four space-time
dimensions are considered, thus encompassing N = 2 and N = 8 theories.
