In cells lacking the histone methyltransferase Set2, initiation of RNA polymerase II transcription occurs inappropriately within the protein-coding regions of genes, rather than being restricted to the proximal promoter. It was previously reported that this "cryptic" transcription occurs preferentially in long genes, and in genes that are infrequently transcribed. Here, we mapped the transcripts produced in an S. cerevisiae strain lacking Set2, and applied rigorous statistical methods to identify sites of cryptic transcription at high resolution. We find that suppression of cryptic transcription occurs independent of gene length or transcriptional frequency. Our conclusions differ with those reported previously because we obtained a higher-resolution dataset, we accounted for the fact that gene length and transcriptional frequency are not independent variables, and we accounted for several ascertainment biases that make cryptic transcription easier to detect in long, infrequently transcribed genes. These new results and conclusions have implications for many commonly used genomic analysis approaches, and for the evolution of high-fidelity RNA polymerase II transcriptional initiation in eukaryotes.