Summary Sleep apnoea is associated with negative outcomes following general anaesthesia. Current recommendations suggest using short‐acting anaesthetic agents in preference to standard agents to reduce this risk, but there is currently no evidence to support this. This randomised controlled triple‐blind trial tested the hypothesis that a combination of short‐acting agents (desflurane‐remifentanil) would reduce the postoperative impact of general anaesthesia on sleep apnoea severity compared with standard agents (sevoflurane‐fentanyl). Sixty patients undergoing hip arthroplasty under general anaesthesia were randomised to anaesthesia with desflurane‐remifentanil or sevoflurane‐fentanyl. Respiratory polygraphy was performed before surgery and on the first and third postoperative nights. The primary outcome was the supine apnoea‐hypopnoea index on the first postoperative night. Secondary outcomes were the supine apnoea‐hypopnoea index on the third postoperative night, and the oxygen desaturation index on the first and third postoperative nights. Additional outcomes included intravenous morphine equivalent consumption and pain scores on postoperative days 1, 2 and 3. Pre‐operative sleep study data were similar between groups. Mean (95%CI) values for the supine apnoea‐hypopnoea index on the first postoperative night were 18.9 (12.7–25.0) and 21.4 (14.2–28.7) events.h −1 , respectively, in the short‐acting and standard anaesthesia groups (p = 0.64). Corresponding values on the third postoperative night were 28.1 (15.8–40.3) and 38.0 (18.3–57.6) events.h −1 (p = 0.34). Secondary sleep‐ and pain‐related outcomes were generally similar in the two groups. In conclusion, short‐acting anaesthetic agents did not reduce the impact of general anaesthesia on sleep apnoea severity compared with standard agents. These data should prompt an update of current recommendations.