Background: Hyperglycemia is associated with increased morbidity and mortality in patients with an acute myocardial infarction (AMI). We evaluated whether complications after AMI are associated with absolute or relative glycemia. Methods: A total of 192 patients with AMI were randomized to intensive or conventional insulin therapy. Absolute glycemia was defined as mean blood glucose level (BGL) during the first 24 h following randomization. Relative glycemia was defined by the stress hyperglycaemia ratio (SHR), calculated as mean BGL divided by average glucose concentration over the prior 3 months estimated from glycosylated haemoglobin. The primary endpoint was a "complicated AMI", defined as an AMI complicated by death, congestive cardiac failure, arrhythmia, cardiac arrest, reinfarction, cardiogenic shock, inotrope use or emergency revascularization. Results: There was not a significant association between mean BGL and complicated AMI (odds ratio (OR) 1.05 per mmol/L glucose increment, 95% confidence intervals (CI) 0.93-1.19). In contrast, SHR was positively associated with a complicated myocardial infarction (OR 1.22 per 0.1 SHR increment, 95% CI 1.06-1.42), and individual complications of death (OR 1.55, 95% CI 1.14-2.11), congestive cardiac failure (OR 1.27, 95% CI 1.05-1.54), arrhythmia (OR 1.31, 95% CI 1.12-1.54) and cardiogenic shock (OR 1.42, 95% CI 1.03-1.97). The relationship between SHR and a complicated AMI was independent of diabetic status, intensive insulin therapy, sex and hypoglycemia. Conclusions: Relative, but not absolute, glycemia during insulin treatment is independently associated with complications after an AMI. Future studies should investigate whether basing therapeutic glycaemic targets on relative glycemia improves patient outcomes.