  We classify all the decomposition matrices of the generic Hecke algebras on 3
strands in characteristic 0. These are the generic Hecke algebras associated to
the exceptional complex reflection groups $G_4$, $G_8$ and $G_{16}$. We prove
that for every choice of the parameters that define these algebras, all
ordinary representations are obtained as modular reductions of irreducible
representations.
