  We report on measurements of three-body recombination rates in an ultracold
gas of $^7$Li atoms in the extremely nonuniversal regime where the two-body
scattering length vanishes. We show that the rate is well defined and can be
described by two-body parameters only: the scattering length $a$ and the
effective range $R_e$. We find the rate to be energy independent, and, by
connecting our results with previously reported measurements in the universal
limit, we cover the behavior of the three-body recombination in the whole range
from weak to strong two-body interactions. We identify a nontrivial magnetic
field value in the nonuniversal regime where the rate should be strongly
reduced.
