  We derive a universal formula for the rate constant \beta for relaxation of a
shallow dimer into deeply-bound diatomic molecules in the case of atoms with a
large scattering length a. We show that \beta is determined by a and by two
3-body parameters that also determine the binding energies and widths of Efimov
states. The rate constant \beta scales like \hbar a/m near the resonance, but
the coefficient is a periodic function of ln(a) that may have resonant
enhancement at values of a that differ by multiples of 22.7.
