  We report an optical spectroscopy study on the newly discovered
superconductor Cu$_{0.07}$TiSe$_2$. Consistent with the development from a
semimetal or semiconductor with a very small indirect energy gap upon doping
TiSe$_2$, it is found that the compound has a low carrier density. Most
remarkably, the study reveals a substantial shift of the "screened" plasma edge
in reflectance towards high energy with decreasing temperature. This
phenomenon, rarely seen in metals, indicates either a sizeable increase of the
conducting carrier concentration or/and a decrease of the effective mass of
carriers with reducing temperature. We attribute the shift primarily to the
later effect.
