Outlier removal is a critical part of feature-based point cloud registration. In this article, we revisit the model generation and selection of the classic RANSAC approach for fast and robust point cloud registration. For the model generation, we propose a second-order spatial compatibility (SC 2) measure to compute the similarity between correspondences. It takes into account global compatibility instead of local consistency, allowing for more distinctive clustering between inliers and outliers at an early stage. The proposed measure promises to find a certain number of outlier-free consensus sets using fewer samplings, making the model generation more efficient. For the model selection, we propose a new Feature and Spatial consistency constrained Truncated Chamfer Distance (FS-TCD) metric for evaluating the generated models. It considers the alignment quality, the feature matching properness, and the spatial consistency constraint simultaneously, enabling the correct model to be selected even when the inlier rate of the putative correspondence set is extremely low. Extensive experiments are carried out to investigate the performance of our method. In addition, we also experimentally prove that the proposed SC 2 measure and the FS-TCD metric are general and can be easily plugged into deep learning based frameworks.