Cell-based studies of human ribonucleases traditionally rely on methods that deplete proteins slowly. We engineered cells in which the 3'→5' exoribonucleases of the exosome complex, DIS3 and EXOSC10, can be rapidly eliminated to assess their immediate roles in nuclear RNA biology. The loss of DIS3 has the greatest impact, causing the substantial accumulation of thousands of transcripts within 60 min. These transcripts include enhancer RNAs, promoter upstream transcripts (PROMPTs), and products of premature cleavage and polyadenylation (PCPA). These transcripts are unaffected by the rapid loss of EXOSC10, suggesting that they are rarely targeted to it. More direct detection of EXOSC10-bound transcripts revealed its substrates to prominently include short 3' extended ribosomal and small nucleolar RNAs. Finally, the 5'→3' exoribonuclease, XRN2, has little activity on exosome substrates, but its elimination uncovers different mechanisms for the early termination of transcription from protein-coding gene promoters. Copyright © 2019 The Author(s). Published by Elsevier Inc. All rights reserved.