  We show that in see-saw models with small or even vanishing lepton mixing
angle $\theta_{12}$, maximal $\theta_{23}$, zero $\theta_{13}$ and zero CP
phases at the GUT scale, the currently favored LMA solution of the solar
neutrino problem can be obtained in a rather natural way by Renormalization
Group effects. We find that most of the running takes place in the energy
ranges above and between the see-saw scales, unless the charged lepton Yukawa
couplings are large, which would correspond to a large $\tan \beta$ in the
Minimal Supersymmetric Standard Model (MSSM). The Renormalization Group
evolution of the solar mixing angle $\theta_{12}$ is generically larger than
the evolution of $\theta_{13}$ and $\theta_{23}$. A large enhancement occurs
for an inverted mass hierarchy and for a regular mass hierarchy with $|m_2 -
m_1| \ll |m_2 + m_1|$. We present numerical examples of the evolution of the
lepton mixing angles in the Standard Model and the MSSM, in which the current
best-fit values of the LMA mixing angles are produced with vanishing solar
mixing angle $\theta_{12}$ at the GUT scale.
