A new three-zone heat extraction system and its analytical model for maximizing the thermal power output of salt gradient solar ponds against a given volume is proposed. The present study considers internal heat exchangers installed within the non-convective zone (NCZ), lower-convective zone (LCZ), and the ground below the pond. The work is validated against a simplified version of the model (eliminating ground and bottom-zone heat extractions) available in the existing literature. Contrary to the conventional practice of optimizing only the middle-zone pond thickness, here, the newly proposed expression is used to find ideal values of both the middle- and bottom-zone thicknesses of the pond along with its cross-sectional area. The present work acknowledges that although the three-zone heat extraction system is the best, yet if a choice for two-zone heat extraction is to be made between the NCZ–LCZ and ground–LCZ, then the former is a better alternative. The power output is observed to increase asymptotically with mass flow rates of the three heat exchangers. However, their values must lie much below their theoretical asymptotic limits and their selection is regulated by constructional and operational constraints. These involve a minimum pond depth to offset surface evaporation, ground seepage water loss, and constraints preventing turbulent flow in heat exchangers to reduce friction loss and pumping power. This work recommends using three heat exchangers instead of either one or two and provides cardinal guidelines to extract heat in an ideal manner for a fixed solar pond volume.