An ultrasonic method is presented which combines features of the differential path and the phase comparison methods. The proposed differential path phase comparison method, referred to as the 'hybrid' method for brevity, eliminates errors resulting from phase changes in the bond between the sample and buffer rod. Define r(P) R(P)> as the square of the normalized frequency for cancellation of sample waves for shear N as the number of wavelengths in twice the sample length. The pressure derivatives r'(P) and R'(P) for samples of Alcoa 2024-T4 aluminum were obtained by using the phase comparison and the hydrid methods. The values of the pressure derivatives obtained by using the phase comparison method show variations by as much as 40% for small values of N (N<50). The pressure derivatives as determined from the hybrid method are reproducible to within ¿2% independent of N. The values of the pressure derivatives determined by the phase comparison method for large N are the same as those determined by the hybrid method. Advantages of the hybrid method are (1) no pressure dependent phase shift at the buffer-sample interface, (2) elimination of deviatoric stress in the sample portion of the sample assembly with application of hydrostatic pressure, and (3) operation at lower ultrasonic frequencies (for comparable sample lengths), which eliminates detrimental high frequency ultrasonic problems. A reduction of the uncertainties of the pressure derivatives of single crystals and of low porosity polycrystals permits extrapolation of such experimental data to deeper mantle depths.