Details of the experimental measurement of collisional relaxation from the upper vibrational states of HD are presented. Direct overtone pumping of HD inv= 4,5, and 6 was accomplished with a pulsed visible wavelength dye laser. The change in translational energy due to collisional relaxation is measured as a function of time by a sensitive pressure transducer placed at the cell wall. Data for vibrational relaxation in pure HD and in HD:4He mixtures are presented.