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We study three-atom inelastic scattering in ultracold ^39K near a Feshbach resonance of intermediate coupling strength. The nonuniversal character of such resonance leads to an abnormally large Efimov absolute length scale and a relatively small effective range r_e, allowing the features of the ^39K Efimov spectrum to be better isolated from the short-range physics. Meticulous characterization of and correction for finite-temperature effects ensure high accuracy on the measurements of these features at large-magnitude scattering lengths.
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