A new apparatus for the measurement of liquid densities at high pressures is presented. The instrument is a development of a vibrating-wire densimeter described earlier and uses the buoyancy force exerted by the sample fluid on an immersed buoy to alter the tension of a wire from which it is suspended. The tension of the wire is related to its resonant frequency under steady-state transverse vibrations through a rigorous theoretical model which includes a complete analysis of the hydrodynamic effect of the fluid surrounding the wire. The present instrument uses a new design for the measuring cell with the purpose of relieving the degeneracy of perpendicular oscillation modes of the vibrating wire. The modifications lead to a significant increase in the precision of the results. Tests performed on the new apparatus and the operating procedure used, which requires the determination of one cell parameter from one density datum at atmospheric pressure, are described. New results for the density of liquid 2,2,4-trimethylpentane at temperatures from 298.15 to 348.15 K and pressures up to 100 MPa are presented. The data obtained have a precision of ±0.05% at a 2a level and an estimated accuracy of approximately ±0.1%.