  A simple $\pi \pi$, $\bar{K}K$, and $\rho \rho$($\omega \omega$) fully
coupled channel model is proposed to predict the isoscalar S-wave phase shifts
and inelasticities for $\pi \pi$ scattering in the 1.0 to 2.0 GeV region. The
S-matrix is required to exhibit poles corresponding to the established
isoscalar J$^{\pi}$ = 0$^+$ resonances f$_0$(975), f$_0$(1400), and
f$_0$(1710). A dominant feature of the experimental $\pi \pi$ inelasticity is
the clear opening of the $\bar{K}K$ channel near 1 GeV, and the opening of
another channel in the 1.4 - 1.5 GeV region. The success of our model in
predicting this observed dramatic energy dependence indicates that the effect
of multi-pion channels is adequately described by the $\pi \pi$ coupling to the
$\bar{K}K$ channel, the $\rho \rho$(4$\pi$) and $\omega \omega$(6$\pi$)
channels.
