Involution products in Coxeter groups

For W a Coxeter group, let W = {w is an element of W vertical bar w = xy where x, y is an element of W and x(2) = 1 = y(2)}. It is well known that if W is finite then W = W. Suppose that w is an element of W. Then the minimum value of l(x) + l(y) - l(w), where x, y is an element of W with w = xy and x(2) = 1 = y(2), is called the excess of w (l is the length function of W). The main result established here is that w is always W-conjugate to an element with excess equal to zero.