The use of calcines of natural limestones as CO2 regenerable sorbents is investigated in this work by studying the decay of the maximum carbonation conversion during many carbonation/calcination cycles. New experimental information is complemented with a compilation of previously published data on this subject. The observed conversion limits in the reaction of CO2 with lime are interpreted in terms of a certain loss in the porosity associated with small pores and a certain increase in the porosity associated with large pores. In the carbonation part of every cycle, the CaCO3 fills up all the available porosity made up of small pores plus a small fraction of the large voids, limited by the thickness of the product layer that marks the onset of the slow carbonation rate. A simple model based on textural changes, observed by scanning electron microscopy, fits equally well all the data from this work and from other authors. The two model parameters are consistent with known mechanism occurring during calcination and carbonation.