  We investigate the tunneling shot noise limits on the sensitivity of a
micromechanical displacement detector based on a metal junction,
radio-frequency single-electron transistor (rf-SET). In contrast with the
charge sensitivity of the rf-SET electrometer, the displacement sensitivity
improves with increasing gate voltage bias and, with a suitably optimized
rf-SET, displacement sensitivities of $10^{-6} {\rm\AA}/\sqrt{\rm Hz}$ may be
possible.
