Brillouin-scattering-based sensors are capable of measuring either the strain or the temperature along the length of an optical fiber in a distributed fashion through measurement of the Brillouin-frequency shift. The cross sensitivity of the frequency shift to these two parameters makes it impossible to differentiate between them by measurement of the frequency shift alone. We report on a new technique that permits the simultaneous measurement of strain and temperature to resolutions of +/-178 microepsilon and +/-3.9 degrees C at a spatial resolution of 3.5 m by incorporation of the Brillouin-loss peak power with the conventional Brillouin-frequency measurement.