The Ssy1-Ptr3-Ssy5 (SPS)-sensing pathway enables yeast to respond to extracellular amino acids. Stp1, the effector transcription factor, is synthesized as a latent cytoplasmic precursor with an N-terminal regulatory domain that restricts its nuclear accumulation. The negative regulatory mechanisms impinging on the N-terminal domain are poorly understood. However, Stp1 latency depends on three inner nuclear membrane proteins, Asi1, Asi2, and Asi3. We report that the N-terminal domain of Stp1 contains a small motif, designated RI, that fully accounts for latency. RI is modular, mediates interactions with the plasma membrane, and can retain histone Htb2 in the cytoplasm. A novel class of STP1 mutations affecting RI were isolated that are less efficiently retained in the cytoplasm but remain under tight negative control by the Asi proteins. Intriguingly, these mutant proteins exhibit enhanced stability in strains lacking ASI1. Our results indicate that RI mediates latency by two distinct activities: it functions as a cytoplasmic retention determinant and an Asi-dependent degron. These findings provide novel insights into the SPS-sensing pathway and demonstrate for the first time that the inner nuclear membrane Asi proteins function in a degradation pathway in the nucleus.