UPMNS = U†ℓUv

We consider corrections to vanishing U e3 and maximal atmospheric neutrino mixing originating from the relation U = U † l U v , where U is the PMNS mixing matrix and U l (U v ) is associated with the diagonalization of the charged lepton (neutrino) mass matrix. We assume that in the limit of U l or U v being the unit matrix, one has U e3 = 0 and θ 23 = π/4, while the solar neutrino mixing angle is a free parameter. Well-known special cases of the indicated scenario are the bimaximal and tri-bimaximal mixing schemes. If U e3 ≢ 0 and θ 23 ≢π/4 due to corrections from the charged leptons, |U e3 | can be sizable (close to the existing upper limit) and we find that the value of the solar neutrino mixing angle is linked to the magnitude of CP violation in neutrino oscillations. In the alternative case of the neutrino sector correcting U e3 = 0 and θ 23 = π/4, we obtain a generically smaller |U e3 | than in the first case. Now the magnitude of CP violation in neutrino oscillations is connected to the value of the atmospheric neutrino mixing angle θ 23 . We find that both cases are in agreement with present observations. We also introduce parametrization independent "sum-rules" for the oscillation parameters.