Equilibrium geometries of quasi two-dimensional jellium systems are ca
lculated in the local density approximation, closely following the ''U
ltimate Jellium Model'' of [1]. The background charge is assumed to be
fully deformable in a layer between two parallel planes, whereas the
wave functions in the direction perpendicular to such a ''Jellium slic
e'' are confined to their ground state. Like for jellium clusters in t
hree dimensions [1], we find that for various system sizes, a trend to
wards a breaking of axial and inversion symmetries is observable.