Following the observation of Killworth that the time-mean velocity in FRAM was self-similar in the vertical, several papers have developed circulation theories of the Southern Ocean assuming such a structure. This paper seeks to create a consistent equivalent-barotropic solution for flow in part of the Southern Ocean, based on an expansion in which the northward variation of Coriolis parameter f is, in a sense, fairly weak. Such a solution only holds in regions of closed contours of a certain characteristic function of f and depth H (the equivalent-barotropic version of f/H, wherein the dependence on H is considerably weakened). Inside these contours, which roughly delineate the Antarctic Circumpolar Current, the flow is strong and takes the equivalent-barotropic form, with all quantities approximately constant along the characteristic, including density below the mixed layer. The theory assumes the vertical structure has been determined by matching with a global solution. The ACC strength can be determined, given the topography and the vertical structure, from a linear second-order ordinary differential equation, under either of two assumptions: that the topography varies weakly with position, or that the horizontal flow is weak at depth. Solutions are not shown here, as they would be similar in form, but cannot be identical to, those of Krupitsky et al. (1996). Instead, the predictions of the theory are compared with OCCAM output. Excellent agreement is found. As in FRAM, the horizontal velocity at all depths is self-similar, but only within the closed-contour region of the ACC. The characteristic function can be deduced from the shape of the self-similar velocity profile. Contours of free surface height and density at any depth overlay well, and these contours lie along contours of the characteristic function as predicted. Local term balances agree well with FRAM analyses by Wells and de Cuevas (1995), but integrated balances do not.