We have measured the binding energy of 7 Li Feshbach molecules deep into the nonuniversal regime by associating atoms in a Bose-Einstein condensate with a modulated magnetic field. We extract the scattering length from these measurements, correcting for nonuniversal short-range effects using the field-dependent effective range. With this more precise determination of the Feshbach resonance parameters we reanalyze our previous data on the location of atom loss features produced by the Efimov effect [Pollack et al., Science 326, 1683]. We find the measured locations of the three-and four-body Efimov features to be consistent with universal theory at the 20%-30% level. Efimov showed more than 40 years ago that three particles interacting via resonant two-body interactions could form an infinite series of three-body bound states as the two-body s-wave scattering length a was varied [1]. In the limit of zero-range interactions, the ratios of scattering lengths corresponding to the appearance of each bound state were predicted to be a universal constant, equal to approximately 22.7. The only definitive observations of the Efimov effect have been in ultracold atoms, where the ability to tune a via a Feshbach resonance [2,3] has proven to be essential. Since the first evidence for Efimov trimers was obtained in ultracold Cs [4], experiments have revealed both three-and four-body Efimov states in several atomic species. Although the Efimov effect has now been confirmed, several open questions remain, including a full understanding of the role of nonuniversal finite-range effects. Accurate comparisons with theory require that these nonuniversal contributions be quantitatively determined and incorporated.We previously characterized the F = 1,m F = 1 Feshbach resonance in 7 Li, which is located at approximately 738 G, by extracting a from the measured size of trapped Bose-Einstein condensates (BEC) assuming a mean-field Thomas-Fermi density distribution [5,6]. These data were fit to obtain a(B), the function giving a versus magnetic field, which was used to assign values of a to Efimov features observed in the rate of inelastic three-and four-body loss of trapped atoms [5]. More recently, two groups have characterized the same Feshbach resonance by directly measuring the binding energy, E b , of the weakly bound dimers on the a > 0 side of the Feshbach resonance [7][8][9]. These measurements disagree with our previous measurements based on BEC size. The disagreement in the parameters characterizing the Feshbach parameters is sufficiently large to affect the comparison of the measured Efimov features with universal theory.In this paper, we report measurements of E b , which we fit to obtain a(B). The measurement of E b has fewer systematic uncertainties than the BEC size measurement, which is affected at large scattering length by beyond meanfield effects and by anharmonic contributions to the trapping potential. The extraction of a from E b can therefore be more accurate, and unlike the condensate size measurement, E b is r...