Barocaloric materials show thermal changes near non-isochoric ferroic phase transitions [1]. These thermal changes are giant near first-order phase transitions where both the volume change and the entropy change across the transition are large. However, the existence of temperature and pressure hysteresis in these giant barocaloric materials is detrimental for their application in sustained cooling cycles [1]. Here I will screen the state-of-the-art giant barocaloric materials in terms of temperature and pressure hysteresis, and will discuss strategies to minimise the corresponding loss in cooling efficiency.