In the late eighties, H. R. Morton in [Math. Proc. Camb. Philos. Soc. 99, 107–109 (1986; Zbl 0588.57008)] and J. Franks and R. F. Williams in [Trans. Am. Math. Soc. 303, 97–108 (1987; Zbl 0647.57002)] showed that for any braid \(\beta\) on \(n\) strands with exponent sum \(w\) the number \(w-n+1\) provides a lower bound for the minimal \(v\)-degree of the Homfly polynomial of the closure of the braid and the number \(w+n-1\) provides an upper bound for the maximal \(v\)-degree of the Homfly polynomial of the closure of the braid. Thus the braid index enables us to bound the \(v\)-degrees of the nontrivial terms of the Homfly polynomial. In the paper reviewed here, the author shows that for any such braid \(\beta\) the coefficient of \(v^{w-n+1}\) in the Homfly polynomial of the closure of \(\beta\) agrees with \((-1)^{n-1}\) times the coefficient of \(v^{w+n^2-1}\) in the Homfly polynomial of the closure of \(\beta \Delta^2\), where \(\Delta\) is the Garside half-twist braid. Thus the lower bound for the \(v\)-degree of the Homfly polynomial for the closure of \(\beta\) given by Morton, Franks, and Williams is sharp if and only if the upper bound is sharp for the closure of \(\beta \Delta^2\).