Design debugging has become a resource-intensive bottleneck in modern VLSI CAD flows, consuming as much as 60% of the total verification effort. With typical design sizes exceeding the half-million synthesized gates mark, the growing number of blocks to be examined dramatically slows down the debugging process. The aim of this work is to prune the number of debugging iterations for finding all potential bugs, without affecting the debugging resolution. This is achieved by using structural dominance relationships between circuit components. More specifically, an iterative fixpoint algorithm is presented for finding dominance relationships between multiple-output blocks of the design. These relationships are then leveraged for the early discovery of potential bugs, along with their corrections, resulting in significant debugging speed-ups. Extensive experiments on real industrial designs show that 66% of solutions are discovered early due to dominator implications. This results in consistent performance gains in all cases and a 1.7x overall speed-up for finding all potential bugs, demonstrating the robustness and practicality of the proposed approach.