  We give a simple necessary and sufficient condition for a Schubert variety
$X_w$ to be smooth when $w$ is a freely braided element of a simply laced Weyl
group; such elements were introduced by the authors in a previous work
(math.CO/0301104). This generalizes in one direction a result of Fan concerning
varieties indexed by short-braid avoiding elements. We also derive generating
functions for the freely braided elements that index smooth Schubert varieties.
All results are stated and proved only for the simply laced case.
