Compensation is indispensable in inductive-power-transfer (IPT) converters, facilitating the characteristics of nearly zero reactive circulating power, soft switching realization and the required load-independent constant-voltage (CV) or constant-current (CC) output to improve the transfer efficiency and decrease the component ratings. However, the load-independent output relies on the IPT parameters greatly. The space-constrained IPT transformer poses a limitation on the design of the IPT converter transfer function and makes the IPT converter hard to optimize. This paper will analyze the design freedom of the double-sided LC compensation circuit from the points of load-independent constant output and zero reactive power. A thorough derivation is given for the double-sided LC compensation with CC output not constrained by the transformer parameters. The output CC design boundary is also stated. Then an LC-CC compensation topology is proposed to generate the flexible CC output compensating the output current amplitude limitation of double-sided LC compensation.