In the 1970's, Efimov showed that if nonrelativistic particles have strong resonant 2-body interactions, the low-energy observables in the 3-body sector are universal, independent of the details of the 2-body potential. For example, in the resonant limmit, there is a sequence of 3-body bound states whose binding energies differ by multiplicative factors of 515. Efimov's results apply strictly only if there are no deeply-bound 2-body states. I will explain how Efimov's results are modified by the existence of deep 2-body bound states. These effects are likely to be observed in experiments on Bose-Einstein condensates of alkali atoms.