Using the MHD equilibrium equations and assuming simple current profiles and various limiter configurations, the authors have investigated the ellipticity attainable in a straight magnetic quadrupole field. It is found that for certain presciptions of parameters there are two values of ellipticity b/a. In practice only the lower value is expected to be realizable; its maximum value depends on current profile and choice of limiter and, for the models used here, lies between 1.0 and 2.9. For the prescriptions which lead to a single ellipticity, the upper limit to b/a is set by the intervention of the separatrix, and for the present models a value of approximately 2.0 has been obtained.