  Meson-meson amplitudes are important on their own and also play key roles in
analyses of heavy-meson and tau decays. In this work we propose a new
phenomenological model suited to all $SU(3)$ mesonic two-body final state
interactions up to energies around 2 GeV. It is aimed at replacing those
entering the old isobar model, produced in the 1960's, long before the
development of QCD. The only similarity between our new proposal and amplitudes
used in the isobar model concern vector resonances in the elastic regime. In
other situations, especially those involving scalar resonances and coupled
channels, the isobar model is not compatible with post-QCD dynamics. In order
to support these claims convincingly and to motivate our approach, we consider
applications to the $\pi \pi $ amplitude and compare our version with the
isobar model in several different instances. We also show that the new model
provides a clear indication of the mechanism responsible for the sharp rise
observed in the $\pi\pi$ phase around $1\,$ GeV. The phenomenological
amplitudes proposed here are suited to any number of resonances in a given
channel and rely just on masses and coupling constants as free parameters.
Concerning theory, they incorporate chiral symmetry at low energies, include
coupled channels and respect unitarity whenever appropriate.
