The demand for better air conditioning in buildings is increasing from year to year. Compression machines are normally used for cold-air production, due to their compactness and favourable price. Sorption machines are used in special cases only, covering small niches of the cooling market. In our paper a three-stage cascading sorption cycle is proposed, consisting of a bottoming double-effect absorption cycle with a LiBr/H2O working pair and a topping solid-gas cycle with CaO/H2O as the working pair. Because water is used as the refrigerant in the topping cycle the evaporation pressure level is low, what results in the insufficient intensity of the synthesis phase relative to the decomposition phase. As a solution, two modifications of the topping cycle are proposed in which the evaporation pressure level is increased to intensify the synthesis phase. It is shown that coefficient of performance (COP) values of 1.6 could be reached, despite the fact that the topping cycle is not used as a cooling cycle anymore. The COP value represents an improvement of about 30% compared to industrial double-effect LiBr/H2O absorption chillers currently on the market.