Moment matching approximations (MMAs) are arguably the most popular method to approximate the distribution of aggregate risk. The existing MMAs comprise such naïve methods as the normal and shifted-gamma approximations that, respectively, match the first two and three moments. More intricate methods are based on the mixed Erlang distributions. However, in practice the sums of risks can have numerous and just a few summands; in the latter case the normal approximation is very questionable. Also, in practice the distributions of the stand-alone risks can be light-tailed or heavy-tailed. In the latter case moments of higher orders may not exist, and so the approximation based on mixed Erlang distributions is of limited usefulness. I will reveal a refined MMA method that approximates the distributions of interest to any precision, works well for light and heavy-tailed distributions, and is fast irrespective of the number of the involved summands.