The dependence of the exciton binding energy on the structural parameters in T-shaped quantum wires is studied numerically, including nonparabolicity and dielectric mismatch. The symmetric structure with pure AlAs barriers was found to give the highest exciton binding energy. Optimized asymmetric T-structures show a binding energy that is nearly constant in a large range of parameters. A large single-particle confinement does not necessarily lead to a large exciton binding energy. A weak correlation is observed between the maximum of the binding energy and the localization of the uncorrelated electron wave function.