Leading Order Textures for Lepton Mass Matrices

In theories with three light neutrinos, certain simplicity assumptions allow the construction of a complete list of leading order lepton mass matrices. These matrices are consistent with m_{tau} \neq 0, Delta m^2_{12} \ll Delta m^2_{23}, theta_{23} approx 1, and theta_{13} = 0, as suggested by measurements of atmospheric and solar neutrino fluxes. The list contains twelve generic cases: two have three degenerate neutrinos, eight have two neutrinos forming a Dirac state, and in only two cases is one neutrino much heavier than the other two. For each of these twelve generic cases the possible forms for the perturbations which yield m_{mu} are given. Ten special textures are also found.