  We explore the possibilities for extending the sensitivity of current
searches for the charged lepton flavor violating decays $\mu\ -> e \gamma$ and
$\mu\ -> eee$. A future facility such as Project X at Fermilab could provide a
much more intense stopping $\mu^+$ beam, facilitating more sensitive searches,
but improved detectors will be required as well. Current searches are limited
by accidental and physics backgrounds, as well as by the total number of
stopped muons. One of the limiting factors in current detectors for $\mu\ -> e
\gamma$ searches is the photon energy resolution of the calorimeter. We present
a new fast Monte Carlo simulation of a conceptual design of a new experimental
concept that detects converted $e^+e^-$ pairs from signal photons, taking
advantage of the improved energy resolution of a pair spectrometer based on a
silicon charged particle tracker. We also study a related detector design for a
next generation $\mu\to eee$ search experiment.
