The author studies the effects of dielectric screening on scattering rates due to electron-phonon interactions in quasi-one-dimensional quantum-well wires. He considers the interaction of confined electrons with bulk polar-optical and acoustic phonons. Acoustic phonons are examined, both in the deformation potential and the piezoelectric couplings. Screening effects are included via a temperature-dependent dielectric function epsilon T(q) in the random-phase approximation, by renormalizing the electron-phonon interaction. Numerical results are given for the GaAs system in the quantum-size limit where a lowering of screened electron-phonon scattering rates is found. The effects of screening are most significant for the electron-optical-phonon interaction.