We study the predictions for CP phases and absolute neutrino mass scale for broad classes of models with a U(2)-like flavor symmetry. For this purpose we consider the same special textures in neutrino and charged lepton mass matrices that are successful in the quark sector. While in the neutrino sector the U(2) structure enforces two texture zeros, the contribution of the charged lepton sector to the Pontecorvo-Maki–Nakagawa–Sakata (PMNS) matrix can be parametrized by two rotation angles. Restricting to the cases where at least one of these angles is small, we obtain three representative scenarios. In all scenarios we obtain a narrow prediction for the sum of neutrino masses in the range of 60–75 meV, possibly in the reach of upcoming galaxy survey experiments. All scenarios can be excluded if near-future experimental date provide evidence for either neutrinoless double-beta decay or inverted neutrino mass ordering.