Termination of transcription by RNA polymerase II (Pol II) is a poorly understood yet essential step in eukaryotic gene expression. Termination of pre-mRNA synthesis is coupled to recognition of RNA signals that direct cleavage and polyadenylation of the nascent transcript. Termination of nonpolyadenylated transcripts made by Pol II in the yeast Saccharomyces cerevisiae, including the small nuclear and small nucleolar RNAs, requires distinct RNA elements recognized by the Nrd1 protein and other factors. We have used genetic selection to characterize the terminator of the SNR13 snoRNA gene, revealing a bipartite structure consisting of an upstream element closely matching a Nrd1-binding sequence and a downstream element similar to a cleavage/polyadenylation signal. Genome-wide selection for factors influencing recogniton of the SNR13 terminator yielded mutations in the gene coding for the essential Pol II-binding protein Ssu72. Ssu72 has recently been found to associate with the pre-mRNA cleavage/polyadenylation machinery, and we find that an ssu72 mutation that disrupts Nrd1-dependent termination also results in deficient poly(A)-dependent termination. These findings extend the parallels between the two termination pathways and suggest that they share a common mechanism to signal Pol II termination.