  Taking the supersymmetric inverse seesaw mechanism as the explanation for
neutrino oscillation data, we investigate charged lepton flavor violation in
radiative and 3-body lepton decays as well as in neutrinoless $\mu-e$
conversion in muonic atoms. In contrast to former studies, we take into account
all possible contributions: supersymmetric as well as non-supersymmetric. We
take CMSSM-like boundary conditions for the soft supersymmetry breaking
parameters. We find several regions where cancellations between various
contributions exist, reducing the lepton flavor violating rates by an order of
magnitude compared to the case where only the dominant contribution is taken
into account. This is in particular important for the correct interpretation of
existing data as well as for estimating the reach of near future experiments
where the sensitivity will be improved by one to two orders of magnitude.
Moreover, we demonstrate that ratios like BR($\tau\to 3 \mu$)/BR($\tau\to \mu
e^+ e^-$) can be used to determine whether the supersymmetric contributions
dominate over the $W^\pm$ and $H^\pm$ contributions or vice versa.
