Pre-rRNA processing generates mature 18S, 5.8S and 28S/25S rRNAs through multistage removal of surrounding 5′-ETS/3′-ETS and intervening ITS1/ITS2 segments. Endonucleolytic activities release by-products, which need to be eliminated. Here, we investigated the interplay of exosome-associated 3′-5′ exonucleases DIS3 and RRP6 in rRNA processing and by-product elimination in human cells. In agreement with previous reports, we observed accumulation of 5.8S and 18S precursors upon dysfunction of these enzymes. However, none of these phenotypes was so pronounced as previously overlooked accumulation of short RNA species derived from 5′-ETS (01/A’-A0), in cells with non-functional DIS3. We demonstrate that removal of 01/A’-A0 is independent of the XRN2 5′-3′ exonucleolytic activity. Instead, it proceeds rapidly after A0 cleavage and occurs exclusively in the 3′-5′ direction in several phases – following initiation by an unknown nuclease, the decay is executed by RRP6 with some contribution of DIS3, whereas the ultimate phase involves predominantly DIS3. Our data shed new light onto the role of human exosome in 5′-ETS removal. Furthermore, although 01/A’-A0 degradation involves action of two nucleases associated with the exosome ring, similar to 5.8S 3′-end maturation, it is likely that contrary to the latter process, RRP6 acts prior to, or redundantly with DIS3.