The large quantities of reactor-grade (RG) and weapons-grade (WG) Pu accumulated worldwide could be reduced by employing 100% mixed-oxide (MOX) cores in light water reactors. The buildup of new Pu from the U present in the MOX, however remains disadvantageous from the viewpoint of inventory reduction and also enhances the need for multiple recycling. A more effective way would be to use U-free fuel so that no new Pu is produced. A comparison is made, from the physics design viewpoint, between the potential and the possible difficulties for two different types of Pu-burning pressurized water reactor cores, namely, 100% MOX and 100% uranium-free Pu fuel. The latter employs ZrO2 as inert matrix and Er2O3 as burnable poison. In each case, RG and WG Pu have been considered separately. The characteristics of the four different cores have been studied on the basis of three-dimensional calculations for an equilibrium cycle, a real-life UO2-fueled core being considered as reference for comparison purposes. For all four Pu-burning cases, it appears possible to design a four-region core with a natural cycle length of more than 300 days. For the 100% MOX cores, the Pu mass is reduced during irradiation by ~35% of the initial Pu inventory. For the U-free cores, the consumption is about twice as much, i.e., ~60% for the RG-Pu fuel and over 70% for the WG-Pu core. The reactivity balance in going from hot full power to hot zero power conditions shows that while the 100% MOX core with RG Pu would need more effective control rods, both types of U-free cores have larger shutdown margins than the reference case. Consideration of the reactivity coefficients indicates that a steam-line-break accident could be more problematic in the MOX core with RG Pu than in the other cases. The rod ejection transient should be safe because the maximum inserted worth of a control rod is ~0.5 $. More detailed investigations of transient behavior-particularly for the U-free cores-are needed, the current study having considered feasibility mainly from the viewpoint of static physics considerations