Double hybrid heat pumps, systems, and methods of operation that provide increased efficiency in both heating and cooling modes, heated water, and other advantages. The system includes a compressor for compressing low-pressure vapor phase refrigerant to high-pressure vapor phase refrigerant, a refrigerant condensing heat exchanger to heat water and cool the refrigerant to a high-pressure liquid refrigerant, which is provided to a refrigerant cooling heat exchanger in which any remaining high-pressure vapor phase refrigerant is condensed and the high-pressure liquid refrigerant is further cooled. The high-pressure cooled liquid refrigerant is passed through an expansion valve to drop the pressure of the cooled liquid to yield a low-pressure cooled liquid refrigerant or low-pressure cooled two-phase refrigerant. The low-pressure cooled liquid or two-phase refrigerant is then evaporated in a refrigerant evaporating heat exchanger to produce the low-pressure vapor refrigerant that is returned to the compressor.