The binding energy of excitons and biexcitons and the exciton dephasing in T-shaped GaAs quantum wires is investigated by transient four-wave mixing. The T-shaped structure is fabricated by cleaved-edge overgrowth, and its geometry is engineered to optimize the one-dimensional confinement. In this wire of 6.6 ϫ24 nm 2 size, we find a one-dimensional confinement of more than 20 meV, an inhomogeneous broadening of 3.4 meV, an exciton binding energy of 12 meV, and a biexciton binding energy of 2.0 meV. A dispersion of the homogeneous linewidth within the inhomogeneous broadening due to phonon-assisted relaxation is observed. The exciton acoustic-phonon-scattering coefficient of 6.1Ϯ0.5 eV/K is larger than in comparable quantum-well structures. ͓S0163-1829͑99͒04147-8͔