  We reproduce the hierarchy of link invariants associated to the series of
$N$-state vertex models with a method different from the original construction
due to Akutsu, Deguchi and Wadati. The alternative method substitutes the
`crossing symmetry' property exhibited by the Boltzmann weights of the vertex
models by a similar property which, for the purpose of constructing link
invariants, encodes the same information but requires only the limit of the
Boltzmann weights when the spectral parameter is sent to infinity.
