We measured half-lives of 21,248 mRNA 3' isoforms in yeast by rapidly depleting RNA polymerase II from the nucleus and performing direct RNA sequencing throughout the decay process. Interestingly, half-lives of mRNA isoforms from the same gene, including nearly identical isoforms, often vary widely. Based on clusters of isoforms with different half-lives, we identify hundreds of sequences conferring stabilization or destabilization upon mRNAs terminating downstream. One class of stabilizing element is a polyU sequence that can interact with poly(A) tails, inhibit the association of poly(A)-binding protein, and confer increased stability upon introduction into ectopic transcripts. More generally, destabilizing and stabilizing elements are linked to the propensity of the poly(A) tail to engage in double-stranded structures. Isoforms engineered to fold into 3' stem-loop structures not involving the poly(A) tail exhibit even longer half-lives. We suggest that double-stranded structures at 3' ends are a major determinant of mRNA stability.