A new method is presented to extrapolate experimental vapor pressures down to the triple point. The method involves a nonlinear regression analysis based on the Clausius-Clapeyron equation and a simple relation for the enthalpy of vaporization. Triple-point pressures and vapor pressures up to 0.1-0.2 MPa are estimated for R125, R32, R143a, R134a, R152a, R123, R124, and ammonia; they generally agree with available experimental data within their uncertainty. Equations for the enthalpy of vaporization which describe this property fairly well at low temperatures are obtained as a byproduct.