  A non-relativistic system of three identical particles will display a rich
set of universal features known as Efimov physics if the scattering length a is
much larger than the range l of the underlying two-body interaction. An
appropriate effective theory facilitates the derivation of both results in the
|a| goes to infinity limit and finite-l/a corrections to observables of
interest. Here we use such an effective-theory treatment to consider the impact
of corrections linear in the two-body effective range, r_s on the three-boson
bound-state spectrum and recombination rate for |a| much greater than |r_s|. We
do this by first deriving results appropriate to the strict limit |a| goes to
infinity in coordinate space. We then extend these results to finite a using
once-subtracted momentum-space integral equations. We also discuss the
implications of our results for experiments that probe three-body recombination
in Bose-Einstein condensates near a Feshbach resonance.
