  Bose-Einstein condensates of 10$^4$ $^{85}$Rb atoms in a cylindrical trap are
studied using a recently proposed modified Gross-Pitaevskii equation. The
existence of a Feshbach resonance allows for widely tuning the scattering
length of the atoms, and values of the peak gas parameter, $x_{pk}$, of the
order of 10$^{-2}$ can be attained. We find large differences between the
results of the modified Gross-Pitaevskii and of the standard Thomas-Fermi, and
Gross-Pitaevskii equations in this region. The column densities at $z=0$ may
differ by as much as $\sim 30%$ and the half maximum radius by $\sim 20%$. The
scattering lengths estimated by fitting the half maximum radius within
different approaches can differ by $\sim 40%$.
