  In this paper we give a new and simplified proof of the theorem on selection
of standing waves for small energy solutions of the nonlinear Schr\"odinger
equations (NLS) that we gave in \cite{CM15APDE}. We consider a NLS with a
Schr\"odinger operator with several eigenvalues, with corresponding families of
small standing waves, and we show that any small energy solution converges to
the orbit of a time periodic solution plus a scattering term. The novel idea is
to consider the "refined profile", a quasi--periodic function in time which
almost solves the NLS and encodes the discrete modes of a solution. The refined
profile, obtained by elementary means, gives us directly an optimal coordinate
system, avoiding the normal form arguments in \cite{CM15APDE}, giving us also a
better understanding of the Fermi Golden Rule.
