Since detection of an RNA molecule is the major criterion to define transcriptional activity, the fraction of the genome that is expressed is generally considered to parallel the complexity of the transcriptome. We show here that several supposedly silent intergenic regions in the genome of S. cerevisiae are actually transcribed by RNA polymerase II, suggesting that the expressed fraction of the genome is higher than anticipated. Surprisingly, however, RNAs originating from these regions are rapidly degraded by the combined action of the exosome and a new poly(A) polymerase activity that is defined by the Trf4 protein and one of two RNA binding proteins, Air1p or Air2p. We show that such a polyadenylation-assisted degradation mechanism is also responsible for the degradation of several Pol I and Pol III transcripts. Our data strongly support the existence of a posttranscriptional quality control mechanism limiting inappropriate expression of genetic information.