We study a number of models, based on a non-Abelian discrete group, that su
ccessfully reproduce the simple and predictive Yukawa textures usually asso
ciated with U(2) theories of flavor. These models allow for solutions to th
e solar and atmospheric neutrino problems that do not require altering succ
essful predictions for the charged fermions or introducing sterile neutrino
s. Although Yukawa matrices are hierarchical in the models we consider, the
mixing between second- and third-generation neutrinos is naturally large.
We first present a quantitative analysis of a minimal model proposed in ear
lier work, consisting of a global fit to fermion masses and mixing angles,
including the most important renormalization group effects. We then propose
two new variant models: The first reproduces all important features of the
SU(5) x U(2) unified theory with neither SU(5) nor U(2). The second demons
trates that discrete subgroups of SU(2) can be used in constructing viable
supersymmetric theories of flavor without scalar universality even though S
U(2) by itself cannot.