  We show that it is possible to extend Moore's analysis of the classical
scattering amplitudes of the bosonic string to those of the N=1 superstring.
Using the bracket relations we are able to show that all possible amplitudes
involving both bosonic and fermionic string states at arbitrary mass levels can
be expressed in terms of amplitudes involving only massless states. A slight
generalization of Moore's original definition of the bracket also allows us to
determine the 4-point massless amplitudes themselves using only the bracket
relations and the usual assumptions of analyticity. We suggest that this should
be possible for the higher point massless amplitudes as well.
