Since its discovery by Berkovits 25 years ago, the pure-spinor formulation of the superstring has proven to be a very useful tool in the calculation of scattering amplitudes, both at tree- and loop-level. However, almost all of its applications are confined to the scattering of massless states. Computation of massive string amplitudes is possible in principle, but difficult to perform within the usual pure-spinor prescription. In this talk, I will report progress on computing manifestly super-Poincare invariant amplitudes through an alternative procedure, which does not explicitly involve the pure-spinor variable and should apply equally well to massless and massive external states.