Two new ReBCO-CORC® based cable-in-conduit conductors (CICC) are developed by CERN in collaboration with ACT-Boulder. Both conductors feature a critical current of about 80 kA at 4.5 K and 12 T. One conductor is designed for operation in large detector magnets, while the other is aimed for application in fusion type magnets. The conductors use a six-around-one cable geometry with six flexible ReBCO CORC® strands twisted around a central tube. The fusion CICC is designed to be cooled by the internal forced flow of either helium gas or supercritical helium to cope with high heat loads in superconducting magnets in large fusion experimental reactors. In addition, the cable is enclosed by a stainless steel jacket to accommodate with the high level of Lorentz forces present in such magnets. Detector type magnets require stable, high-current conductors. Therefore, the detector CORC® CICC comprises an OFHC copper jacket with external conduction cooling, which is advantageous due to its simplicity. A 2.8 m long sample of each conductor is manufactured and prepared for testing in the Sultan facility at PSI Villigen. In the paper, the conductor design and assembly steps for both CORC® CICCs are highlighted.