  We present a new method, exact in $\alpha'$, to explicitly compute string
tree-level amplitudes involving one massive state and any number of massless
ones. This construction relies on the so-called twisted heterotic string, which
admits only gauge multiplets, a gravitational multiplet, and a single massive
supermultiplet in its spectrum. In this simplified model, we determine the
moduli-space integrand of all amplitudes with one massive state using
Berends-Giele currents of the gauge multiplet. These integrands are then
straightforwardly mapped to gravitational amplitudes in the twisted heterotic
string and to the corresponding massive amplitudes of the conventional type-I
and type-II superstrings.
