Strains carrying rna14.1 and rna15.2 mutations are defective in pre-mRNA 3' cleavage, polyadenylation, and transcription termination. Long extended read-through transcripts generated in rna14.1 and rna15.2 strains are greatly stabilized by depletion of Rrp41p, a core component of the exosome complex or the RNA helicase Dob1p/Mtr4p. The absence of the nuclear-specific exosome component, Rrp6p, from the rna14.1 strain gave a very different phenotype. Short polyadenylated pre-mRNAs were strongly stabilized, and these were functional for translation. Production of these mRNAs was suppressed by depletion of Rrp41p, indicating that they are the products of exosome processing followed by uncoupled polyadenylation. The balance between complete degradation of 3'-unprocessed pre-mRNAs and their processing to functional mRNAs is regulated, with degradation favored on glucose media.