We show that in see-saw models with small or even vanishing lepton mixing angle Θ12, maximal Θ23, zero Θ13 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 β in the Minimal Supersymmetric Standard Model (MSSM). The Renormalization Group evolution of the solar mixing angle Θ12 is generically larger than the evolution of Θ13 and Θ23. A large enhancement occurs for an inverted mass hierarchy and for a regular mass hierarchy with |m2 - m1| « |m2 + 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 Θ12 at the GUT scale. © SISSA/ISAS 2002.