We present an on-going project consisting of analysis of a sample of twenty-five metal-poor stars, most of them carbon-enriched and thus tagged carbon-enhanced metal-poor (CEMP) stars, observed with the high-resolution HERMES spectrograph mounted on the Mercator telescope (La Palma), the UVES spectrograph on VLT (ESO Chile), or the HIRES spectrograph on KECK (Hawaii). This sample consists of CEMP-s stars, which are CEMP stars enriched in slow-neutron-capture (s-process) elements, as well as CEMP-rs stars enriched with both s-process and rapid-neutron-capture (r-process) elements. We also included an r-process-enriched star for comparison purposes. The origin of the abundance differences between CEMP-s and CEMP-rs stars is presently unknown. It has been claimed that the i-process (intermediate nucleosynthesis process), whose site still remains to be identified, could better reproduce CEMP-rs abundances than the s-process. We aim at understanding whether the i-process and its putative site can reproduce the abundance pattern measured in CEMP-rs stars.