In view of getting insights into the molecular determinants of the binding efficiency of intrinsically disordered proteins (IDPs), we used random mutagenesis. As a proof of concept, we chose the interaction between the intrinsically disordered C-terminal domain of the measles virus nucleoprotein (NTAIL) and the X domain (XD) of the viral phosphoprotein and assessed how amino acids substitutions introduced at random within NTAIL affect partner recognition. In contrast with directed evolution approaches, we did not apply any selection and used the gene library approach not for production purposes but for achieving a better understanding of the NTAIL/XD interaction. For that reason, and to differentiate our approach from similar approaches that make use of systematic (i.e. targeted) mutagenesis, we propose to call it "descriptive random mutagenesis" (DRM). NTAIL variants generated by error-prone PCR were picked at random in the absence of selection pressure, and characterized in terms of sequence and binding abilities towards XD. DRM identified determinants of NTAIL/XD interaction that were in good agreement with previous work, but also provided new insights. In particular, we discovered that the primary interaction site is poorly evolvable in terms of binding abilities towards XD. We also identified a critical NTAIL residue whose role in stabilizing the NTAIL/XD complex had previously escaped detection, and identified NTAIL regulatory sites that dampen the interaction while being located outside the primary interaction site. Results show that DRM is a valuable approach to study binding abilities of IDPs.