  We present a simple method of removing the singularities associated with soft
photon emission to all orders in perturbation theory through exponentiation,
while keeping a consistent description of hard photon emission. We apply this
method to the process e+ e- --> mu+ mu- + n photons where we include both Z^0
and photon exchange and retain the muon mass dependence. The photonic radiation
is allowed to be radiated off any charged leg, and so we include all initial
and final state radiation, as well as all interference effects. The effect of
exponentiation is to suppress soft photon emission over the cross-section you
would obtain from working at strictly leading order. We also show how one would
extend the method to treat the collinear singularity; and remove the associated
leading mass logarithms.
