  We construct analytical supersymmetric coloured black hole solutions, i.e.
non-Abelian black hole solutions that have no asymptotic non-Abelian charge but
do have non-Abelian charges on the horizon that contribute to the
Bekenstein-Hawking entropy, to two SU(3)-gauged N=2 d= supergravities. The
analytical construction is made possible due to the fact that the main
ingredient is the Bogomol'nyi equation, which under the assumption of spherical
symmetry admits a Lax pair formulation. The Lax matrix needed for the coloured
black holes must be defective which, even though it is the non-generic and less
studied case, is a minor hindrance.
