That or Which, which is the word that is best

My advisor, Henry Kautz, offers this bit of wisdom that somehow I missed in my years of schooling. In addition to being a world-class AI researcher, he also has some creative writing credibility, so I would expect he could know such a bit of information. The question is, When do you use "which" and when do you use "that"?

"that" is restrictive -- a necessary property, selects out which of the noun (solutions) are desired
"which" is non-restrictive -- incidental property of the noun

Compare:

1. "Solutions that avoid stigma are best."
   ==> restrictive, there are many solutions, but only the ones that avoid stigma are best.
2. Solutions proposed by Patterson, which avoid stigma, are best.
   ==> non-restriction, must be the case that ALL of Patterson's solutions are best.
3. Solutions proposed by Patterson that avoid stigma are best.
   ==> restrictive, only those solutions by Patterson that also avoid stigma are the best ones. Patterson may also have solutions that include stigma.

Note use of commas in (2) but no commas in (3).