We derive the exact, factorized, purely elastic scattering matrices fo
r the a2n-1(2) family of nonsimply-laced affine Toda theories. The der
ivation takes into account the distortion of the classical mass spectr
um by radiative corrections, as well as modifications of the usual boo
tstrap assumptions since for these theories anomalous threshold singul
arities lead to a displacement of some single particle poles.