Using an upward thermal diffusion cloud chamber specially designed for operation at elevated pressures and temperatures, we have observed a dependence of homogeneous nucleation of methanol, ethanol, 2-propanol, and 1-propanol on the total pressure of nucleating vapor and background gas. This dependence is manifested by increasing values of the measured critical supersaturation with increasing total pressure. This dependence implies that the homogeneous nucleation rate of these substances decreases as total pressure increases. We have observed a dependence on the nature of the background gas. The effect of increasing total pressure is different using helium, hydrogen, or nitrogen. We have also observed that the dependence of the critical supersaturation on total pressure (as manifested by the slope of the critical supersaturation vs total pressure data at constant temperature) is temperature dependent.