Pervasive and hidden transcription is widespread in eukaryotes, but its global level, the mechanisms from which it originates and its functional significance are unclear. Cryptic unstable transcripts (CUTs) were recently described as a principal class of RNA polymerase II transcripts in Saccharomyces cerevisiae. These transcripts are targeted for degradation immediately after synthesis by the action of the Nrd1-exosome-TRAMP complexes. Although CUT degradation mechanisms have been analysed in detail, the genome-wide distribution at the nucleotide resolution and the prevalence of CUTs are unknown. Here we report the first high-resolution genomic map of CUTs in yeast, revealing a class of potentially functional CUTs and the intrinsic bidirectional nature of eukaryotic promoters. An RNA fraction highly enriched in CUTs was analysed by a 3' Long-SAGE (serial analysis of gene expression) approach adapted to deep sequencing. The resulting detailed genomic map of CUTs revealed that they derive from extremely widespread and very well defined transcription units and do not result from unspecific transcriptional noise. Moreover, the transcription of CUTs predominantly arises within nucleosome-free regions, most of which correspond to promoter regions of bona fide genes. Some of the CUTs start upstream from messenger RNAs and overlap their 5' end. Our study of glycolysis genes, as well as recent results from the literature, indicate that such concurrent transcription is potentially associated with regulatory mechanisms. Our data reveal numerous new CUTs with such a potential regulatory role. However, most of the identified CUTs corresponded to transcripts divergent from the promoter regions of genes, indicating that they represent by-products of divergent transcription occurring at many and possibly most promoters. Eukaryotic promoter regions are thus intrinsically bidirectional, a fundamental property that escaped previous analyses because in most cases divergent transcription generates short-lived unstable transcripts present at very low steady-state levels.