Interferometers with M paths are studied. It is shown that the accuracy of the phase-shift measurement can be improved by increasing the number of paths. For a detection scheme that uses coherent input states, phase sensitivity rescales as \ensuremath{\Delta}\ensuremath{\varphi}\ensuremath{\propto}${\mathrm{M}}^{\mathrm{\ensuremath{-}}1}$, and nonunit quantum efficiency \ensuremath{\eta} at detectors only decreases the effective M by a factor $\sqrt{\ensuremath{\eta}}$.