We have measured details of the quasi-one-dimensional (Q1D) Fermi-surface sections in the organic superconductor κ-(BEDT-TTF)2Cu(NCS)2 and its deuterated analogue using angle-dependent millimetre-wave techniques. There are differences in the corrugations of the Fermi surfaces in the deuterated and undeuterated salts. We suggest that this is important in understanding how deuteration affects the superconducting transition temperature. The data suggest that the 'nestability' of the Q1D Fermi sheets may be important in understanding the 'universal' phase diagram of κ-(BEDT-TTF)2X, in agreement with other recent studies. The experiments also support models for superconductivity which invoke electron–electron interactions depending on the topological properties of the Fermi surface.