HTS CrossConductor is a compact stacked-tape REBCO conductor of high current density. In this contribution, a non-concentric three-phase cable design based on HTS CroCos is presented, which offers the possibility to reduce the cable diameter significantly. One of the important aspects of HTS-AC power cables are the AC-losses, which are investigated both theoretically and experimentally. For the measurement of the dissipated power loss in both single-phase and three-phase conductor arrangements, a calorimetric method is used. The results indicate that it is possible to reduce the outer cable diameter compared to concentric cables designs by a factor of two. When the losses of such a cable with HTS CroCo design shall not exceed 2 W/m for all three-phases, the maximum ampacity results in a current of 600 A(rms) per phase. Depending of the target there are many potential applications for such an ultra-compact HTS CroCo-based power transmission cable design.