To identify and investigate the mechanisms of electron-phonon (e-ph) relaxation in weakly disordered metallic conductors, we measure the electron dephasing rate in a series of suspended and supported 15-nm thick AuPd wires. In a wide temperature range, from ∼8 K to above 20 K, the e-ph interaction dominates in the dephasing processes. The corresponding relaxation rate reveals a quadratic temperature dependence, τ(e-ph)(-1)=A(ep)T2, where A(ep)≈5×10(9) K(-2) s(-1) is essentially the same for all samples studied. Our observations are shown to be in good agreement with the theory which predicts that, even in weakly disordered metallic structures at moderately low temperatures, the major mechanism of the e-ph relaxation is the electron scattering from vibrating defects and impurities.