A new and simple calibration technique that greatly enhances the measurement sensitivity of conventional fiber-optic reflectometry based on Fresnel reflection from the tip of a fiber is used for demonstrating the feasibility of measuring solute concentrations and index changes in fluids to very high precision. The amplitude of pulses originating from reflection from the fiber-fluid interface is compared in real-time with the amplitude of reference pulses from a fiber-air interface such that errors caused by pulse amplitude fluctuations and slightly varying detector responses are corrected. Using solutions of salt and water, it is demonstrated that the technique is capable of measuring index changes of about $1 { imes} 10^{-5}$ corresponding to a salt concentrations of 0.01 %.