  We study perturbations of exactly tri-bimaximal neutrino mixings under the
assumption that they are coming solely from the charged lepton mass matrix.
This may be plausible in scenarios where the mass generation mechanisms of
neutrinos and charged leptons/quarks have a different origin. As a working
hypothesis, we assume mass textures which may be generated by the
Froggatt-Nielsen mechanism for the charged lepton and quark sectors, which
generically leads to strong hierarchies, whereas the neutrino sector is exactly
tri-bimaximal with a mild (normal) hierarchy. We find that in this approach,
deviations from maximal atmospheric mixing can be introduced without affecting
theta_13 and theta_12, whereas a deviation of theta_13 or theta_12 from its
tri-bimaximal value will inevitably lead to a similar-sized deviation of the
other parameter. Therefore, the already very precise knowledge of theta_12
points towards small sin^2(2 theta_13) <= 0.01. The magnitude of this deviation
can be controlled by the specific form of the charged lepton texture.
