The possibility of performing Monte Carlo transport calculations using cross-section probability tables on the entire energy spectrum is discussed in this paper. This method possesses straight advantages toward other representations: Self-shielding effects are represented during the random walk in a straightforward way, and the calculation cost remains below continuous-energy simulations. This study takes advantage of previous contributions made in subgroup-based self-shielding models, regarding the definitions of optimized energy meshes and adequate numerical methods for consistently computing cross-section probability tables. Moment-based probability-table cross sections along with an energy mesh comprising only 295 groups lead to results with a similar level of accuracy to those obtained with a continuous-energy Monte Carlo method. Another innovative aspect of this work is related to the introduction of correlated weight matrices into a Monte Carlo algorithm. These correlated weights are used to represent mutual self-shielding effects occurring where resonances of different isotopes overlap.