The principal limitation to precision and accuracy in the bubble solution method for measuring diffusion coefficients of gases in liquids arises from free convection. The governing dimensionless parameter is the Grashof number, which indicates that convection effects become less important for small bubbles, low gas solubility, and high liquid viscosity. Precision within 5% is obtainable for bubble diameters less than 0.3 mm, and values of a second dimensionless parameter DC Jut [(diffusion coefficient)(solubility)/(viscosity)] less than 4 X 10-8. Bubble solution data in pure liquids and in polymer solutions substantiate these conclusions, though the measured values of D appear to be higher than current literature values. The method is particularly suitable for polymer solutions and the data suggest that polymer volume fraction, rather than solution viscosity, is the controlling parameter for diffusion of small molecules in these media.