The electron states of weakly-one-dimensional quantum wires are computed using the adiabatic approximation in the framework of the k . p theory and the envelope-function approximation. The computed transition rates of electrons from one confined state to any other, mediated by the longitudinal optical (LO) phonons, are clearly ordered with respect to the quantum numbers of the states provided by the adiabatic approximation. The average single electron relaxation time from an excited level is shown to either increase or surprisingly decrease as a function of initial energy. Finally, the relaxation dynamics of an excited population of electrons is analyzed. We show that a fast phenomenological intrasubband thermalization, simultaneous to the LO phonon-mediated relaxation, lowers the final average energy and may in some cases significantly speed up the whole relaxation.