The authors study resonant rescattering corrections to the Deck amplitude B for diffractive dissociation of hadrons. The results of numerical calculations for a variety of physically-reasonable forms of B show that provided B falls off faster than a simple pole the rescattered amplitude is well approximated by the form Be^{i delta} cos delta , rather than Be^{i delta} sin delta /k. They conclude that the former expression is generally relevant to situations in which the Born amplitude B is spatially diffuse, while the latter applies if B is spatially localised.