The hollow-cathode effect (HCE) is studied for conventional and modified hollow-cathode discharges (HCDs). HCDs are considered that operate at substantial current densities and moderate voltages (e.g. in a conventional HCD, >1 mA cm^-2 and <400 V, respectively), which are typical of the HCDs in common use. A simple kinetic model is developed and used to predict that the HCE exists even if a small fraction of the total ionization occurs in the cathode-fall regions (CF). The HCE results from ionization becoming more efficient in the negative glow (NG) so that no significant ionization is required to occur in the CF. Consequently, the size of the CF diminishes and a large increase in current takes place. The main features of the HCE are reproduced and good agreement with experiment is found. The results suggest that low-slope-resistance voltage-current characteristics are realized when the ionization in the CF is small. It is next demonstrated that the ions play an important role and that even a small increase in the ion flux from the NG to the CF can contribute to the HCE. The principal geometrical criteria for the conventional and modified HCDs are presented. A segmented HCD tube is considered to study an interesting transition from a conventional HCD through a modified HCD to an abnormal glow discharge. Finally, the principal physical mechanisms which determine the operating characteristics of the modified HCD are identified and discussed.