Equilibrium and axisymmetric stability (n = 0) of a straight, uniform-current plasma maintained by a quadrupole field are considered. Holding all currents constant and keeping the plasma cross-sectional area invariant, the authors investigate the first and second variations of the free energy of the system. The equilibrium is shown to be a vertical ellipse, which recovers previously known results. Unlike earlier work based on the energy principle, it is found that all poloidal mode numbers can be unstable. On the assumption that the vertical shift (m = 1) is stabilized by feedback, the ellipticity is found to be limited to 2.9 by an m = 2 mode. There is evidence that for more realistic current profiles the value could be much smaller.