Surveys of transcription in many organisms have observed widespread expression of RNAs with no known function, encoded within and between canonical coding genes. The search to distinguish functional RNAs from transcriptional noise represents one of the great challenges in genomic biology. Here we report a next-generation sequencing technique designed to facilitate the inference of function of uncharacterized transcript forms by improving their coverage in sequencing libraries, in parallel with the detection of canonical mRNAs. We piloted this protocol, which is based on the capture of 39 ends of polyadenylated RNAs, in budding yeast. Analysis of transcript ends in coding regions uncovered hundreds of alternative-length coding forms, which harbored a unique sequence motif and showed signatures of regulatory function in particular gene categories; independent single-gene measurements confirmed the differential regulation of short coding forms during heat shock. In addition, our 39-end RNA-seq method applied to wild-type strains detected putative noncoding transcripts previously reported only in RNA surveillance mutants, and many such transcripts showed differential expression in yeast cultures grown under chemical stress. Our results underscore the power of the 39-end protocol to improve detection of noncanonical transcript forms in a sequencing experiment of standard depth, and our findings strongly suggest that many unannotated, polyadenylated RNAs may have as yet uncharacterized regulatory functions.