  We introduce a notion of "freely braided element" for simply laced Coxeter
groups. We show that an arbitrary group element $w$ has at most $2^{N(w)}$
commutation classes of reduced expressions, where $N(w)$ is a certain statistic
defined in terms of the positive roots made negative by $w$. This bound is
achieved if $w$ is freely braided. In the type $A$ setting, we show that the
bound is achieved only for freely braided $w$.
