The differential cross section sigma ( theta ) for neutron elastic scattering from ¹²C and for inelastic scattering from the 4.44 MeV state was measured at 15.57, 16.75 and 17.29 MeV. The sigma ( theta ) data, together with published analysing power A_y( theta ) data, were analysed in the framework of the spherical optical model and in the coupled-channels formalism. It was concluded that the present ¹²C(n,n)¹²C data and published data at higher energies appear to be well suited for determining properties of valence single-particle excitations in ¹¹C and ¹³C via an iterative-moment approach or a dispersive optical-model analysis.