A comparison of the effect of different configurations of the outer conducting surface on the stability of a cylindrical circular plasma of radiusaand lengthLis made. As opposed to the usual configuration of a concentric circular outer conductor, ’’fins’’ or radial conducting surfaces lying on the field lines with the nearest edge a distancecfrom the center of the plasma are considered. The comparison procedure is based upon estimating the difference of the perturbed energy integrals for the various configurations. The usual surface perturbations of the form exp[i(kz±n&Vthgr;)],k∼0 are treated. Fins of zero thickness have no effect on then = 0 mode; however, they do tend to stabilize the importantn = 1 mode. Fora/csufficiently small, radial planes &Vthgr; = 0, &pgr;, and ±&pgr;/2 tend to have the same stabilization effect on then = 1 mode as a concentric outer cylinder of radiusb, whereb∼&sqrt;2c. The interaction between the opposite fins was taken into account.