We study three-atom inelastic scattering in ultracold K-39 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 39 K 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. For a single Feshbach resonance, we unambiguously locate four distinct features in the Efimov structure. Three of these features form ratios that obey the Efimov universal scaling to within 10%, while the fourth feature, occurring at a value of scattering length closest to r(e), instead deviates from the universal value.