A thermodynamic analysis of a simple inverse cycle is proposed as a means to evaluate mixtures of CO2 and four organic substances (propane, iso-butane, dimethyl-ether and propylene) as working fluids. The cycle features an internal heat exchanger and is designed to cool down a finite heat capacity flow on the cold side. The analysis covers trans-critical as well as sub-critical cycles. For each organic substance, the composition is optimized. Flammability is accounted for. Dimethyl-ether (DME) turns out to be the best option, as a relatively low mass fraction of this compound is sufficient for reaching the thermodynamic optimum. In this way, a simple, sub-critical refrigeration system may be obtained featuring a non-flammable working fluid and a significant COP increase with respect to pure CO2.