Within the framework of a systematic study of the electronic structure of palladium alloyed with light interstitials, dilute PdC_x alloys with 0<or=x<or=0.003 were investigated in fields up to 11 T and temperatures down to 1.4K by means of the de Haas-van Alphen effect. Information is obtained about the carbon concentration dependence of the extremal cross-sectional areas of several orbits on the Fermi surface and of the electron relaxation times (Dingle temperatures). The experimental results are compared with previous data for the palladium-boron system and palladium alloyed with hydrogen, deuterium and tritium. On the basis of these experimental results it is concluded that most of the four electrons donated by carbon fill states at the Fermi energy of palladium. The experimental results are well described by an extended defect formalism developed for dilute alloys. This theory shows that the somewhat anomalous behaviour of PdC_x (compared with PdB_x alloys) is due to the stronger localisation of the carbon potential, which in turn is responsible for the relatively weak lattice dilation accompanying carbon absorption in palladium.