  We investigate electron-phonon coupling in a narrow suspended metallic wire,
in which the phonon modes are restricted to one dimension but the electrons
behave three-dimensionally. Explicit theoretical results related to the known
bulk properties are derived. We find out that longitudinal vibration modes can
be cooled by electronic tunnel refrigeration far below the bath temperature
provided the mechanical quality factors of the modes are sufficiently high. The
obtained results apply to feasible experimental configurations.
