Many developments in recent years concern the hybridization of sorption systems with a mechanical compressor. This paper presents an assessment study of different hybrid thermochemical systems used to ensure a cold production. A screening over more than 100 ammonia salts have been done to investigate the different compressor configurations. The compressor can be used to assist the decomposition phase, the synthesis phase or both phases. Two major points are tackled : the modification of the operating range and of the performances of such hybrid systems. This article is intended to be a thermodynamic tool for selecting the most suitable ammoniated salt and compressor operating configuration for a targeted cooling application. Compression-assisted decomposition has already been studied in the scientific literature for thermochemical systems, but not the compression-assisted synthesis for a low-temperature cold production. This latter hybridization extends the operating range of the thermochemical process quite the same way as the assisted decomposition but brings better average performances over the operating range compared to a fully thermally driven system, with higher COP (+8 %), exergetic efficiency (+2 %) and primary energy efficiency (+4 %). The possibility to use a compressor in both phases leads to very interesting performances over a largely extended operating range. In this case, the average exergetic efficiency can be 32 % higher than the average exergetic efficiency of a fully thermally driven system.