Protein degradation is critical for maintaining cellular homeostasis. The 20S proteasome is selective for unfolded, extended polypeptide chains without ubiquitin tags. Sequestration of such segments by protein partners, however, may provide a regulatory mechanism. Here we used the AP-1 complex to study how c-Fos turnover is controlled by interactions with c-Jun. We show that heterodimerization with c-Jun increases c-Fos half-life. Mutations affecting specific contact sites (L165V, L172V) or charge separation (E175D, E189D, K190R) with c-Jun both modulate c-Fos turnover, proportionally to their impact on binding affinity. The fuzzy tail beyond the structured b-HLH/ZIP domain (~165 residues) also contributes to the stabilization of the AP-1 complex, removal of which decreases c-Fos half-life. Thus, protein turnover by 20S proteasome is fine-tuned by both specific and fuzzy interactions, consistently with the previously proposed 'nanny' model.