In the domain of point cloud registration, the coarse-to-fine feature matching paradigm has received significant attention due to its impressive performance. This paradigm involves a two-step process: first, the extraction of multi-level features, and subsequently, the propagation of correspondences from coarse to fine levels. However, this approach faces two notable limitations. Firstly, the use of the Dual Softmax operation may promote one-to-one correspondences between superpoints, inadvertently excluding valuable correspondences. Secondly, it is crucial to closely examine the overlapping areas between point clouds, as only correspondences within these regions decisively determine the actual transformation. Considering these issues, we propose OAAFormer to enhance correspondence quality. On the one hand, we introduce a soft matching mechanism to facilitate the propagation of potentially valuable correspondences from coarse to fine levels. On the other hand, we integrate an overlapping region detection module to minimize mismatches to the greatest extent possible. Furthermore, we introduce a region-wise attention module with linear complexity during the fine-level matching phase, designed to enhance the discriminative capabilities of the extracted features. Tests on the challenging 3DLoMatch benchmark demonstrate that our approach leads to a substantial increase of about 7% in the inlier ratio, as well as an enhancement of 2%–4% in registration recall. Finally, to accelerate the prediction process, we replace the Conventional Random Sample Consensus (RANSAC) algorithm with the selection of a limited yet representative set of high-confidence correspondences, resulting in a 100 times speedup while still maintaining comparable registration performance.