Polyakov's prescription for fermionic closed string amplitudes requires that we integrate over gauge-inequivalent geometries on a 2D supermanifold. These inequivalent geometries are parametrized by a finite-dimensional superspace of moduli. This space is described and an integration measure on it is proposed which comes from gauge-fixing the heterotic string. The measure thus obtained is free of conformal and Lorentz anomalies and so can be used to compute invariant string amplitudes.