We present a highly accurate and efficient, yet simple, two-stage voting scheme for distinguishing inlier 3D correspondences by densely assessing and ranking their local and global geometric consistencies. The strength of the proposed method stems from both the novel idea of post-validated voting set, as well as single-point superimposition transforms, which are computationally cheap and avoid rotational ambiguities. Using a well-known dataset consisting of various 3D models and numerous scenes that include different occlusion rates, the proposed scheme is evaluated against state-of-the-art 3D voting schemes, in terms of both the correspondence PR (precision-recall) AUC (area under curve), and the execution time. A total of 374 experiments were conducted for each method, which involved a combination of four models, 50 scenes, and two down-samplings. The proposed scheme outperforms the state-of-the-art 3D voting schemes in terms of both accuracy and speed. Quantitatively, the proposed scheme scores 97.0% ±12.9% on the PR AUC metric, averaged over all of the experiments, while the two state-of-the-art schemes score 74.2% ±22.2% and 78.3% ±26.4%. Furthermore, the proposed scheme requires only 24.1% ±6.0% of the time consumed by the fastest state-of-the-art scheme. The proposed voting scheme also demonstrates high robustness against occlusions and scarce inliers.