  We apply the new method for constructing integrable Hamiltonian hierarchies
of Lax type equations developed in our previous paper, to show that all
W-algebras W(gl_N,f) carry such a hierarchy. As an application, we show that
all vector constrained KP hierarchies and their matrix generalizations are
obtained from these hierarchies by Dirac reduction, which provides the former
with a bi-Poisson structure.
