Calcium looping is a postcombustion CO2 capture technology that uses CaO as a regenerable solid sorbent. One potential advantage of this technology is that it allows flue gases to be treated with SO2, avoiding the need for a costly desulfurization step. In this work, we study the desulfurization capacity of a circulating fluidized bed (CFB) carbonator reactor in a 30 kW(th) pilot plant that has been used to test CO2 and SO2 cocapture. A simple reactor model is applied to analyze the experimental results obtained and to study the effect of the main variables involved in the process: i.e., the circulation rates of solids and the inventory of active material in the CFB reactor. The results obtained have shown that SO2 capture efficiencies above 0.95 can be achieved in a CFB carbonator even when using a low inventory of active material in the bed. Extreme desulfurization (SO2 emissions below 5-10 ppmv) is thought to be achievable in large scale CFB carbonators designed to capture CO2 with CaO.