The N-degrons, a set of degradation signals recognized by the N-end rule pathway, comprise a protein's destabilizing N-terminal residue and an internal lysine residue. We show that the strength of an N-degron can be markedly increased, without loss of specificity, through the addition of lysine residues. A nearly exhaustive screen was carried out for N-degrons in the lysine (K)-asparagine (N) sequence space of the 14-residue peptides containing either K or N (16 384 different sequences). Of these sequences, 68 were found to function as N-degrons, and three of them were at least as active and specific as any of the previously known N-degrons. All 68 K/N-based N-degrons lacked the lysine at position 2, and all three of the strongest N-degrons contained lysines at positions 3 and 15. The results support a model of the targeting mechanism in which the binding of the E3-E2 complex to the substrate's destabilizing N-terminal residue is followed by a stochastic search for a sterically suitable lysine residue. Our strategy of screening a small library that encompasses the entire sequence space of two amino acids should be of use in many settings, including studies of protein targeting and folding.