The objective of this research is to improve understanding of the combustion of binary fuel mixtures in the vicinity of the critical point. Fiber-supported droplets of mixtures of w-heptane and n-hexadecane, initially 1 mm in diameter, were burned in room-temperature air at pressures from 1 M Pa to 6 M Pa under free-fall microgravity conditions. For most mixtures the total burning time was observed to achieve a minimum value at pressures well above the critical pressure of either of the pure fuels. This behavior is explained in terms of critical mixing conditions of a ternary system consisting of the two fuels and nitrogen. The importance of inert-gas dissolution in the liquid fuel near the critical point is thereby re-emphasized, and nonmonotonic dependence of dissolution on initial fuel composition is demonstrated. The results provide information that can be used to estimate high-pressure burning rates of fuel mixtures.