  The experimental three-atom recombination coefficients of the atomic states
$^{23}$Na$|F=1,m_F=-1>$, $^{87}$Rb$|F=1,m_F=-1>$ and $^{85}$Rb$|F=2,m_F=-2>$,
together with the corresponding two-body scattering lengths, allow predictions
of the trimer bound state energies for such systems in a trap. The
recombination parameter is given as a function of the weakly bound trimer
energies, which are in the interval $ 1<m(a/\hbar)^2 E_3< 6.9$ for large
positive scattering lengths, $a$. The contribution of a deep-bound state to our
prediction, in the case of $^{85}$Rb$|F=2,m_F=-2>$, for a particular trap, is
shown to be relatively small.
