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Scalar spread transform dither modulation (SSTDM), together with its variants, is one of the foremost side-informed data hiding methods. Because of the projection stage of additive spread spectrum (Add-SS), SSTDM achieves the same spreading gain as the former, so that both become robust to additive attacks. We show that the similarities between Add-SS and SSTDM do not extend to the popular cropping attack, since when the removed area increases, performance degrades smoothly for the former but steeply for the latter. This conclusion is arrived at after comparing the analytical expressions derived for both methods. Increasing the size of the projected subspace and using a cubic lattice with repetition coding is shown to be a possible solution to cope with cropping while retaining host interference cancellation.