Measles virus is a highly contagious virus that, despite the existence of an effective vaccine, is a major cause of illness and mortality worldwide. The virus has a negative-sense, single-stranded RNA genome that is encapsidated by the nucleocapsid protein (N) to form a helical ribonucleoprotein complex known as the nucleocapsid. This structure serves as the template for both transcription and replication. Paramyxovirus nucleocapsids are flexible structures, a trait that has hitherto hampered structural analysis even at low resolution. We have investigated the extent of this structural plasticity, using real-space methods to calculate three-dimensional reconstructions of recombinant nucleocapsids from cryo-negative stain transmission electron micrographs. Images of short sections of helix were sorted according to both pitch (the axial rise per turn) and twist (the number of subunits per turn). Our analysis indicates that there is extensive conformational flexibility within these structures, ranging in pitch from 50 Angstrom to 66 Angstrom, while twist varies from at least 13.04 to 13.44 with a greater number of helices comprising around 13.1 subunits per turn. We have also investigated the influence of the C terminus of N on helix conformation, analysing nucleocapsids after having removed this domain by trypsin digestion. We have found that this causes a marked change in both pitch and twist, such that the pitch becomes shorter, ranging from 46 Angstrom to 52 Angstrom, while more helices have a twist of approximately 13.3 subunits per turn. Our findings lead us to propose a mechanism whereby changes in conformation, influenced by interactions between viral or host proteins and the C terminus of N, might have a role in regulating the balance of transcription and replication during virus infection.