  General lowest order perturbations to hermitian squared mass matrices of
leptons are considered away from the tribimaximal (TBM) limit in which a weak
flavor basis with mass diagonal charged leptons is chosen. The three measurable
TBM deviants are expressed linearly in terms of perturbation induced
dimensionless coefficients appearing in the charged lepton and neutrino flavor
eigenstates. With unnatural cancellations assumed to be absent and the charged
lepton perturbation contributions to their flavor eigenstates argued to be
small, we analytically derive the following result. Within lowest order
perturbations, a deviation from maximal atmospheric neutrino mixing and the
amount of CP violation in neutrino oscillations cannot both be large (i.e.
$12$-$17 \% $), posing the challenge of verification to forthcoming experiments
at the intensity frontier.
