The "constant-flux" concept introduced recently is leveraged to distribute magnetic flux to improve energy density, lowering the profile of an inductor. The optimal flux distribution with normalized parameters is identified mathematically, and verified by simulation. It is then applied to reduce the dc resistance of a commercial inductor by a factor of two, keeping the outer dimensions and inductance the same. Thermal-limited current rating is improved by 50%, whereas saturation-limited current rating is improved by 20% thanks to the suppression of flux crowding. The simulation result is verified by measurement results of a prototype under high current bias. I.