EuCARD-2 is a project partly supported by FP7 European Commission aiming at exploring accelerator magnet technology for 20-T dipole operating field. The EuCARD-2 collaboration is liaising with similar programs for high-field magnets in the U.S. and Japan. EuCARD-2 focuses, through the work package 10 “future magnets,” on the development of a 10-kA-class superconducting high-current-density cable suitable for accelerator magnets, for a 5-T stand-alone dipole of 40-mm bore and about 1-m length. After stand-alone testing, the magnet will be inserted in a large bore background dipole, 10-18 T. This paper reports on the design and development of models, which are called Feather0, wound with REBCO Roebel cable. Based on aligned block design to take advantage of the anisotropy of the REBCO tapes, Feather0 is a precursor of Feather2, which should reach the project goals in 2016. Feather0 is planned to be tested both in stand alone and as an insert mounted in the CERN Fresca facility providing 10-T background field. The progress of other designs pursued in the collaboration, one based on classical ϑ layout with Roebel cable and the other based on coil block with stacked tape cable, will be also reported.