  I present a method of calculating the coefficients appearing in the
Jones-Wenzl projections in the Temperley-Lieb algebras. It essentially repeats
the approach of Frenkel and Khovanov published in 1997. I wrote this note
mid-2002, not knowing about their work, but then set it aside upon discovering
their article.
  Recently I decided to dust it off and place it on the arXiv --- hoping the
self-contained and detailed proof I give here may be useful. It's also been
cited a number of times, so I thought it best to give it a permanent home.
  The proof is based upon a simplification of the Wenzl recurrence relation. I
give an example calculation, and compare this method to the formula announced
by Ocneanu and partially proved by Reznikoff. I also describe certain moves on
diagrams which modify their coefficients in a simple way.
