  We show, for each algebraically closed field, the rationality of the
following two moduli spaces: M(3,3) parametrizing pairs (C, \eta) where C has
genus 3 and \eta is a 3-torsion divisor class, respectively of M(3,<3>)
parametrizing pairs (C, <\eta>) as above and where <\eta> is the cyclic
subgroup of order 3 in Pic_0(C) generated by \eta.
