The COMPLETE (Complete vs Culprit-only Revascularization to Treat Multi-vessel Disease After Early PCI for STEMI) trial demonstrated that staged nonculprit lesion percutaneous coronary intervention (PCI) reduced major cardiovascular (CV) events in patients with ST-segment elevation myocardial infarction (STEMI) and multivessel coronary artery disease (CAD). The purpose of this study was to determine the effect of nonculprit-lesion PCI timing on major CV outcomes and also the time course of the benefit of complete revascularization. Following culprit-lesion PCI, 4,041 patients with STEMI and multivessel CAD were randomized to staged nonculprit-lesion PCI or culprit-lesion only PCI. Randomization was stratified according to investigator-planned timing of nonculprit-lesion PCI: during or after the index hospitalization. The first coprimary outcome was the composite of CV death or myocardial infarction (MI). In pre-specified analyses, hazard ratios (HRs) were calculated for each time stratum. Landmark analyses of the entire population were performed within 45 days and after 45 days. For nonculprit-lesion PCI planned during the index hospitalization (actual time: median 1 day), CV death or MI was reduced with complete revascularization compared with culprit-lesion only PCI (HR: 0.77; 95% confidence interval CI: 0.59 to 1.00). For nonculprit lesion PCI planned to occur after hospital discharge (actual time: median 23 days), CV death or MI was also reduced with complete revascularization (HR: 0.69; 95% CI: 0.49 to 0.97; interaction p = 0.62). Landmark analyses demonstrated an HR of 0.86 (95% CI: 0.59 to 1.24) during the first 45 days and 0.69 (95% CI: 0.54 to 0.89) from 45 days to the end of follow-up for intended nonculprit lesion PCI versus culprit lesion only PCI. Among STEMI patients with multivessel disease, the benefit of complete revascularization over culprit-lesion only PCI was consistent irrespective of the investigator-determined timing of nonculprit-lesion intervention. The benefit of complete revascularization on hard clinical outcomes emerged mainly over the long term.