Abstract: Methods and medical uses for determining a dose for a glucagon bolus for administration to patients with diabetes for treating mild or moderate hypoglycaemia, while reducing the risk of, or avoiding, rebound hyperglycaemia are described. This work is based on simulations using pharmacokinetic (PK) and pharmacodynamic (PD) models for glucose, insulin and glucagon to develop an optimum glucagon dosing regimen for treatment of mild or moderate hypoglycaemia depending on ambient insulin levels, while reducing the risk of, or avoiding, rebound hyperglycaemia, for example as may occur when an overly large dose of glucagon is administered to a patient having a hypoglycaemic episode.