  The purpose of this note is to give a refinement of the product formula
proved in [1] for the Poincare polynomial of a smooth Schubert variety in the
flag variety of an algebraic group G over C. This yields a factorization of the
number of elements in a Bruhat interval [e,w] in the Weyl group W of G provided
the Schubert variety associated to w is smooth. This gives an elementary
necessary condition for a Schubert variety in the flag variety to be smooth.
