A nonneutral spheroidal plasma can be settled in a rigid rotor equilibrium inside a closed conducting cell independently of induced image charges on the cell wall if the electrostatic potential distribution on the wall surface is set equal to the sum of the external hyperbolic potential (r(2) - 2z(2)) and the self-potential produced by the plasma. A confinement system equipped with a train of properly biased ring electrodes can approximately generate any axisymmetric potential, including the above field. Experiments on confinement of electron spheroids in such a system showed that the confinement time became the longest when the condition to diminish the image charge effects was satisfied. The observed frequency of the centre-of-mass harmonic oscillation of the plasma in this configuration was in good agreement with the estimated one.