We show how to treat boundary divergences in heterotic string theory covariantly and unambiguously. The method applies even to theories with nonvanishing tadpoles; in this case the Fischler-Susskind mechanism sufficies to ensure well defined answers. Also n-point functions are well defined with no special string-tension renormalizations. As an example we find the loop corrections to the linearized background equations of motion for the O(16)×O(16) string needed to give unambiguous, finite scattering amplitudes. No splitting or projection of supermoduli space is needed.