Non-opioid analgesics, paracetamol, non-steroidal anti-inflammatory drugs (NSAIDs), or cyclo-oxygenase 2 (COX-2) inhibitors are often given along with morphine as part of multimodal analgesia after major surgery. We have undertaken a systematic review and a mixed treatment comparison (MTC) analysis in order to determine explicitly which class of non-opioid analgesic, paracetamol, NSAIDs, or COX-2 inhibitors is the most effective in reducing morphine consumption and morphine-related adverse effects. Sixty relevant studies were identified. The MTC found that when paracetamol, NSAIDs, or COX-2 inhibitors were added to patient-controlled analgesia (PCA) morphine, there was a statistically significant reduction in morphine consumption: paracetamol [mean difference (MD) -6.34 mg; 95% credibility interval (CrI) -9.02, -3.65], NSAIDs (MD -10.18; 95% CrI -11.65, -8.72), and COX-2 inhibitors (MD -10.92; 95% CrI -12.77, -9.08). There was a significant reduction in nausea and postoperative nausea and vomiting with NSAIDs compared with placebo (odds ratio 0.70; 95% CrI 0.53, 0.88) but not for paracetamol or COX-2 inhibitors, nor for NSAIDs compared with paracetamol or COX-2 inhibitors. There was no statistically significant difference in sedation between any intervention and comparator. On the basis of six trials (n=695), 2.4% of participants receiving an NSAID experienced surgical-related bleeding compared with 0.4% with placebo. The MTC found that there is a decrease in 24 h morphine consumption when paracetamol, NSAID, or COX-2 inhibitors are given in addition to PCA morphine after surgery, with no clear difference between them. Similarly, the benefits in terms of reduction in morphine-related adverse effects do not strongly favour one of the three non-opioid analgesics.