We discuss models of neutrino masses that lead to a large mixing angle for atmospheric neutrino oscillations. In particular we study a mechanism where a simple texture for the Dirac matrix leads to the observed pattern of mixings for a continuous range of Majorana matrices in a reasonably natural way. Both nearly maximal and small mixing solutions for solar neutrinos are compatible with this model. Possible dynamical realizations are discussed and a detailed example in terms of horizontal U(1) charges is presented.