Our previous work has shown that the amino-terminal residue of a short-lived protein is a distinct component of the protein's degradation signal. To define the complete signal, otherwise identical dihydrofolate reductase test proteins bearing different extensions and either a "stabilizing" or a "destabilizing" amino-terminal residue were expressed in the yeast S. cerevisiae and their in vivo half-lives compared. The amino-terminal degradation signal is shown to comprise two distinct determinants. One, discovered previously, is the protein's amino-terminal residue. The second determinant, identified in the present work, is a specific lysine residue whose function in the degradation signal is not dependent on the unique amino acid sequences in the vicinity of the residue. The mechanistic significance of the second determinant is illuminated by the finding that in a targeted, short-lived protein, a chain of branched ubiquitin-ubiquitin conjugates is confined to a lysine residue that has been identified in the present work as the second determinant of the degradation signal.