Proper 3' end formation is critical for the production of functional mRNAs. Termination by RNA polymerase II is linked to mRNA cleavage and polyadenylation, but it is less clear whether earlier stages of mRNA production also contribute to transcription termination. We performed a genetic screen to identify mutations that decreased transcriptional readthrough of a defective GAL10 poly(A) terminator. A partial deletion of the GAL10 downstream region leads to transcription through the downstream GAL7 promoter, resulting in the inability of cells to grow on galactose. Mutations in elongation factors Spt4 and Spt6 suppress the readthrough phenotype, presumably by decreasing the amount of polymerase transcribing through the downstream GAL7 promoter. Interestingly, mutations in the mRNA-binding protein Npl3 improve transcription termination. Both in vivo and in vitro experiments suggest that Npl3 can antagonize 3' end formation by competing for RNA binding with polyadenylation/termination factors. These results suggest that elongation rate and mRNA packaging can influence polyadenylation and termination.