Smoke point measurements of diluted methane and ethylene flames were made in a co-flowing laminar jet diffusion flame at pressures up to 8 atm. The smoke point corresponds to the fuel flow rate where the soot production is exactly offset by the soot oxidation, and as such is sensitive to changes in rates of production or oxidation. Flame height in these flames was measured as a function of pressure, diluent, and dilution level as well as both fuel exit velocity profile (i.e., plug or parabolic) and fuel/air velocity ratio. As pressure increases, the smoke point became less sensitive to diluent or dilution level. In addition to heat capacity and thermal diffusivity differences between CO2 and He for example, the large differences in kinematic viscosity was shown to play an important role in the diluent's ability to suppress the fuel's propensity to form soot.