A heat pump water heater has a tank portion, an electric heating structure for adding electrical heat to water stored in the tank, and a heat pump for adding refrigerant heat to the tank water. A control system associated with the water heater has three user-selectable heating modes for heating the tank water during a given heating demand cycle—a first mode that initially heats the tank water with refrigerant heat while the electric heat is locked out for a first predetermined period before supplementing the refrigerant heat if necessary, a second mode similar to the first mode but with a longer electric heat lockout period, and a third mode in which only the electric heat is utilized to satisfy a tank water heating demand. Illustratively, the heat pump is disposed in a compact component arrangement on the top end of the water heater tank.