A hot water system, such as a Domestic Hot Water (DHW) system, combines the best characteristics of a tankless heater and a hot water storage tank to provide superior energy and water savings and safety. The storage tank does not need an internal heat source. Tank hot water may be recovered through the tankless heater. A first control (A) activates hot water recirculation from the storage tank to safely heat pipes to supply, for example, a sink, with no wasted water. The tankless heater supplies a greater demand, such as for a shower or tub. A second control (B) activates a cold-water diverter to the supply from the storage tank to the tankless heater. A water flow sensor keeps the tankless heater as the hot water source until the water flow stops. The so-called cold-water-sandwich is eliminated, and waste of water or heat is reduced.