  We investigate the influence of confinement on the positional order of a
quasi-1D electron system trapped on the surface of liquid helium. We find
evidence that the melting of the Wigner solid (WS) depends on the confinement
strength, as well as electron density and temperature. A reentrant
solid-liquid-solid transition is observed for increasing electron density under
constant electrostatic confinement. As the electron row number $N_y$ changes,
varying commensurability results in a modulation of the WS order, even when
$N_y$ is large (several tens). This is confirmed by Monte Carlo simulations.
