We have evolved a series of 13 complete solar models that utilize different assumed heavy-element compositions. Models that are based upon the heavy-element abundances recently determined by Asplund and coworkers are inconsistent with helioseismological measurements. However, models in which the neon abundance is increased by 0.4 -0.5 dex to log N(Ne) = 8.29 c 0.05 on the scale in which log N(H) = 12 are consistent with the helioseismological measurements even though the other heavy-element abundances are in agreement with the determinations of Asplund et al. These results sharpen and strengthen an earlier study by Antia & Basu. The predicted solar neutrino fluxes are affected by the uncertainties in the composition by less than their 1 s theoretical uncertainties.