  We exploit the decoherence of electrons due to magnetic impurities, studied
via weak localization, to resolve a longstanding question concerning the
classic Kondo systems of Fe impurities in the noble metals gold and silver:
which Kondo-type model yields a realistic description of the relevant multiple
bands, spin and orbital degrees of freedom? Previous studies suggest a fully
screened spin $S$ Kondo model, but the value of $S$ remained ambiguous. We
perform density functional theory calculations that suggest $S = 3/2$. We also
compare previous and new measurements of both the resistivity and decoherence
rate in quasi 1-dimensional wires to numerical renormalization group
predictions for $S=1/2,1$ and 3/2, finding excellent agreement for $S=3/2$.
