  We discuss precision measurements of the leading atmospheric parameters at a
standard neutrino factory with a detector that is sensitive to muons alone. The
oscillation of the muon- and electron neutrinos in the neutrino factory beam to
tau neutrinos adds to the muon events sample (both right sign and wrong sign)
via leptonic decays of the taus produced through charge-current interactions in
the detector. In particular, we study how this affects a precision measurement
of the atmospheric mixing parameters and the deviation of nu_mu <--> nu_tau
mixing from maximality. In spite of the enhancement of the number of events due
to the additional tau contribution, the determination of the atmospheric mixing
angle and the deviation from maximality will be poorer. We show that it is
impossible to devise satisfactory cuts to remove this tau contamination.
Neglect of these tau contributions will lead to an incorrect conclusion about
the precision obtainable at such a neutrino factory.
