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Frequency shifts of a 6328 Å single frequency laser stabilized on the Lamp dip have been measured as a function of total helium-neon pressure and for several gas mixtures. The total shift in the pressure region between 2 and 4 torr is about 40 MHz, with a constant region between 2 and 2.5 torr. A simplified theoretical treatment is given based upon collision broadened phase shifts and line widths determined in other laser experiments. It is shown that the variations in these parameters with pressure form the basis of an adequate prediction of the observed pressure shifts.