The Ski2-Ski3-Ski8 (SKI) complex assists the RNA exosome during the 3’-5’ degradation of cytoplasmic transcripts. Previous reports showed that the SKI complex is involved in the 3’-5’ degradation of mRNA, including 3’ untranslated regions (UTRs), devoid of ribosomes. Paradoxically, we recently showed that the SKI complex directly interacts with ribosomes during the co-translational mRNA decay and that this interaction is necessary for its RNA degradation promoting activity. Here, we characterized a new SKI-associated factor, Ska1, which antagonizes the SKI-ribosome interaction. We showed that the SKI-Ska1-subcomplex is specifically involved in the degradation of ribosome-free RNA regions such as long mRNA 3’UTRs and cytoplasmic lncRNAs. We propose a model in which the SKI-exosome complex first targets ribosome-free RNA 3’ends in its Ska1-associated form. When the complex reaches the mRNA coding sequence, the Ska1-SKI-exosome complex is exchanged for the SKI-exosome, which interacts directly with ribosomes in order to resume the degradation process.