Step 1: Outpatient (day-care) procedures demand an analgesic whose effect wears off quickly, because the goal is same-day discharge with minimal residual sedation or respiratory compromise.
Step 2: Alfentanil satisfies this requirement. It has a rapid onset and the shortest clinical duration among the listed opioids, so analgesia is delivered promptly and clears fast, allowing early ambulation and discharge.
Step 3: Comparing the alternatives: morphine and pethidine linger too long and carry a higher risk of delayed sedation, while fentanyl, though potent, lasts longer than alfentanil and tends to accumulate. None of these match the short turnaround needed in OPD work.
Step 4: Day-care anaesthesia commonly pairs alfentanil with short agents like propofol, midazolam and mivacurium. Hence the answer is alfentanil.
\[\boxed{\text{Alfentanil}}\]