  In this article we analyse, for a simple model, the properties of a practical
implementation of a fully self-consistent theory of adiabatic large-amplitude
collective motion using the local harmonic approach. We show how we can deal
with contaminations arising from spurious modes, caused by standard simplifying
approximations. This is done both at zero and finite angular momentum. We
analyse in detail the nature of the collective coordinate in regions where they
cross spurious modes and mixing is largest.
