In a process for separating at least one “heavy” impurity such as hydrogen sulfide from crude carbon dioxide comprising significant quantities of at least one “light” impurity such as non-condensable gases, involving at least one heat pump cycle using carbon dioxide-containing fluid from the process as the working fluid, the “light” impurity is removed from the crude carbon dioxide and carbon dioxide is subsequently recovered from the removed “light” impurity, thereby improving overall carbon dioxide recovery and efficiency in terms of energy consumption.