Fine dice for a quick-cooking sauce.

The size you cut the individual components of a flavor mixture depends on how long the mixture will cook and if it will be pureed. The French make a big deal out of demanding that a classic mirepoix (Mirepoix is the French name for a pureed. The French make a big deal out of demanding that a classic mirepoix (Mirepoix is the French name for a combination of onions, carrots and celery) be cut into very tiny dice —a handy way of torturing beginning culinary students. But there's actually a sound reason for chopping mirepoix into small pieces for a quick-cooking dish: the smaller pieces will release their flavor more quickly during the short cooking time. On the other hand, mirepoix for a pot of long-simmering stock can consist of very large pieces of vegetables—onions cut in half, whole celery ribs, and carrots in chunks.
Any other Idea?