The structure of a confined fluid of hard circular cylinders confined to a slit is studied using a simple theory in the context of a restricted orientation model; previous work is extended to higher densities. It is shown that, as the density increases, the fluid within the central region of the slit undergoes phase transitions which depend on the ratio,l/d, of the length to the diameter of the cylinders, and these transitions are interpreted in terms of the bulk behaviour of the fluid. Whenl/dis 0·25, the bulk fluid first undergoes a first-order isotropic-nematic transition as the density increases and then makes a transition to a spatially ordered phase. On the other hand whenl/dis 0·8, the fluid undergoes a transition to a spatially ordered phase and does not pass through a nematic phase at all. These results are qualitatively in agreement with results obtained by Frenkel and Mulder from the simulation of hard ellipsoids. The limitations of the model are discussed and suggestions made for modifications to improve upon the quantitative predictions of the model at high densities.