  We calculate one-loop string amplitudes of open and closed strings with
N=1,2,4 supersymmetry in four and six dimensions, by compactification on
Calabi-Yau and K3 orbifolds. In particular, we develop a method to combine
contributions from all spin structures for an arbitrary number of legs at
minimal supersymmetry. Each amplitude is cast into a compact form by
reorganizing the kinematic building blocks and casting the worldsheet integrals
in a basis. Infrared regularization plays an important role to exhibit the
expected factorization limits. We comment on implications for the one-loop
string effective action.
