  In integrable field theories the S-matrix is usually a product of a
relatively simple matrix and a complicated scalar factor. We make an
observation that in many relativistic integrable field theories the scalar
factor can be expressed as a convolution of simple kernels appearing in the
nested levels of the nested Bethe ansatz. We formulate a proposal, up to some
discrete ambiguities, how to reconstruct the scalar factor from the nested
Bethe equations and check it for several relativistic integrable field
theories. We then apply this proposal to the AdS asymptotic Bethe ansatz and
recover the dressing factor in the integral representation of Dorey, Hofman and
Maldacena.
