The present study documents the constructal design and optimization of finned tubes used in air-cooled heat exchangers. The considered tubes are equipped with annular fins. The aim is to minimize the overall thermal resistance by morphing the geometry. The geometrical and thermo-physical parameters considered are the number of fins, ratio of fin height to tube diameter, Stanton number, ratio of fin conductivity to air conductivity, ratio of in-tube fluid conductivity to air conductivity and dimensionless pressure drop. Two constraints are applied in the optimization process: fixed overall volume of heat exchanger and fixed volume fraction of fin material. It is found that there exist optimal values for the number and the height of fins. Moreover, the optimal heat transfer has an extremum in a special volume fraction of fin material.