Refrigeration of a solid-state system with light has potential applications for cooling small-scale electronics and photonics. We show theoretically that two coupled semiconductor quantum wells are efficient cooling media for optical refrigeration because they support long-lived indirect electron-hole pairs. Thermal excitation of these pairs to distinct higher-energy states with faster radiative recombination allows an efficient escape channel to remove thermal energy from the system. This allows reaching much higher cooling efficiencies than with single quantum wells. From band-diagram calculations along with an experimentally realistic level scheme we calculate the cooling efficiency and cooling yield of different devices with coupled quantum wells embedded in a suspended nanomembrane. The dimension and composition of the quantum wells allow optimizing either of these quantities, which cannot, however, be maximized simultaneously. Quantum-well structures with electrical control allow tunability of carrier lifetimes and energy levels so that the cooling efficiency can be optimized over time as the thermal population decreases due to the cooling.