A laser-illuminated Fabry-Perot cavity with a finesse of 83000 and power dissipation of a few μW is tested at room temperature. The sensitivity to changes in the length of the cavity is 5.6× 10-17 m/Hz. The sensitivity of multimode gravitational-wave bar detectors operated between 0.03 and 4.2 K and instrumented with a Fabry-Perot transducer of similar characteristics is calculated. The sensitivity projected for a three-mode 2400-kg Al 5056 antenna operating at 800 Hz and cooled to 0.03 K is δh= 6.8× 10-21 and the noise temperature of the system is a factor of 16 above the standard quantum limit. Such a sensitivity would permit observations of astrophysical significance.© 1992 The American Physical Society.