The work of Xi et al. shows how two-point extrapolations of the CCSD(T) energy can be much more accurate than previously expected if one optimizes the parameters for each pair of basis sets. Here we build on this outstanding work by showing that this higher accuracy can be obtained at even lower cost by choosing the diffuse basis functions more efficiently. Since jul and jun basis sets have less functions than aug, there is a significant reduction in the cost of the calculations. Our first finding is that the jul results are almost the same as the aug results. Our second finding is that jun basis set have either a minimal reduction in accuracy or even an improved accuracy as compared to aug basis sets; since there is a huge reduction in computational cost, we recommend using jun basis sets for CBS calculations with the parameters optimized here rather than using aug basis sets.