The essential helicase-like protein Sen1 mediates termination of RNA Polymerase II (Pol II) transcription at snoRNAs and other noncoding RNAs in yeast. A mutation in the Pol II subunit Rpb1 that increases the elongation rate increases read-through transcription at Sen1-mediated terminators. Termination and growth defects in sen1 mutant cells are partially suppressed by a slowly transcribing Pol II mutant and are exacerbated by a faster-transcribing Pol II mutant. Deletion of the nuclear exosome subunit Rrp6 allows visualization of noncoding RNA intermediates that are terminated but not yet processed. Sen1 mutants or faster-transcribing Pol II increase the average lengths of preprocessed snoRNA, CUT, and SUT transcripts, while slowed Pol II transcription produces shorter transcripts. These connections between transcription rate and Sen1 activity support a model whereby kinetic competition between elongating Pol II and Sen1 helicase establishes the temporal and spatial window for early Pol II termination.