  We study a family of 5-dimensional non-Abelian black holes that can be
obtained by adding an instanton field to the well-known D1D5W Abelian black
holes. Naively, the non-Abelian fields seem to contribute to the black-hole
entropy but not to the mass due to their rapid fall-off at spatial infinity. By
uplifting the 5-dimensional supergravity solution to 10-dimensional Heterotic
Supergravity first and then dualizing it into a Type-I Supergravity solution,
we show that the non-Abelian fields are associated to D5-branes dissolved into
the D9-branes (dual to the Heterotic "gauge 5-branes") and that their
associated RR charge does not, in fact, contribute to the entropy, which only
depends on the number16 pages of D-strings and D5 branes and the momentum along
the D-strings, as in the Abelian case. These "dissolved" or "gauge" D5-branes
do contribute to the mass in the expected form. The correct interpretation of
the 5-dimensional charges in terms of the string-theory objects solves the
non-Abelian hair puzzle, allowing for the microscopic accounting of the
entropy. We discuss the validity of the solution when alpha prime corrections
are taken into account.
