We formulate and discuss a 4-dimensional SUSY version of an A model for tri-bimaximal neutrino mixing which is completely natural. We also study the next-to-the-leading corrections and show that they are small, once the ratios of A breaking VEVs to the cutoff are fixed in a specified interval. We also point out an interesting way of presenting the A group starting from the modular group. In this approach, which could be interesting in itself as an indication on a possible origin of A, the Lagrangian basis where the symmetry is formulated coincides with the basis where the charged leptons are diagonal. If the same classification structure in A is extended from leptons to quarks, the CKM matrix coincides with the unit matrix in leading order and a study of non-leading corrections shows that the departures from unity of the CKM matrix are far too small to accomodate the observed mixing angles.