  Very recently, we proposed an explanation of the discrepancy between the
measured anomalous magnetic moment of the muon and the Standard Model (SM)
prediction in which the dominant contribution to $(g-2)_\mu$ originates in
Kaluza-Klein (KK) excitations (of the lepton gauge boson) which do not mix with
quarks (to lowest order) and therefore can be quite light avoiding LHC
constraints. In this addendum we reexamine the bounds on 4-fermion contact
interactions from precise electroweak measurements and show that the
constraints on KK masses and couplings are more severe than earlier thought.
However, we demonstrate that our explanation remains plausible if a few KK
modes are lighter than LEP energy, because if this were the case the
contribution to the 4-fermion scattering from the internal propagator would be
dominated by the energy and not by the mass. To accommodate the $(g-2)_\mu$
discrepancy we assume that the lepton number $L$ does not partake in the
hypercharge and propagates in one extra dimension (transverse to the SM
branes): for a mass of the lowest KK excitation of 60 GeV (lower than the LEP
energy), the string scale is roughly 10 TeV while the $L$ gauge coupling is of
order $\sim 10^{-1}$.
