  There are reasons to believe that mechanisms exist in the solar interior
which lead to random density perturbations in the resonant region of the Large
Mixing Angle solution to the solar neutrino problem. We find that, in the
presence of these density perturbations, the best fit point in the
(sin^2(2\theta), Delta_m^2) parameter space moves to smaller values, compared
with the values obtained for the standard LMA solution. Combining solar data
with KamLAND results, we find a new compatibility region, which we call
VERY-LOW LMA, where sin^2(2\theta) ~ 0.6 and Delta_m^2~2e-5 eV^2, for random
density fluctuations of order 5% < \xi< 8%. We argue that such values of
density fluctuations are still allowed by helioseismological observations at
small scales of order 10 - 1000 km deep inside the solar core.
