Step 1: Problem
The thin cut-off I was sawing had been sucked down into the blade arbor area and crushed my table saw insert on the way through. Luckily this all happened very quickly and nobody was hurt, but it really alerted me to the fact that there is a better way to use the table saw to to cut thin slices of of wood - get yourself a zero clearance table saw insert.
Zero clearance inserts minimize tear-out, support even the smallest and thinnest of cuts, and even make your table saw safer.
Unfortunately they don't clear dust as well since they leave no room for air to be sucked down if you've got a dust collection system for your table saw, but if you use it just for small detail cuts that doesn't really matter much. The benefits far outweigh the drawbacks on this one.