Results of experimental and numerical studies are presented for a class of horizontal thermal convection in a long box forced at one horizontal boundary by two regions of destabilizing buoyancy flux separated by a region of stabilizing buoyancy flux. The steady-state circulation with zero net heat input is examined. The circulation generally involves two plumes, one at each end of the box, which drive overturning throughout the domain. The flow is classified into three regimes according to the pattern of interior circulation and depending on the relative heat input applied to the two destabilizing regions. Unequal heat inputs can double the interior stratification above that created by symmetric flow with two identical plumes, and when the heat inputs differ by more than 10%, the interior stratification is set by the stronger plume. The arrangement of boundary forcing broadly parallels the distribution of the zonally averaged surface cooling and heating in the Northern and Southern Hemispheres, and the results suggest that ocean overturning circulations may be sensitive to interhemispheric differences in the buoyancy inputs.