Abstract: Surface offsetting is a commonly used technique in CAD and CAGD, and effectively handling self-intersections is crucial for its success. In order to maintain rationality while removing self-intersections in offset surfaces, three geometric adjustment algorithms have been proposed. For surfaces with a single concave region, it has been proven that the shortest distance between the surface and a point on the offset surface can be used to identify self-intersections. Based on the least-squares progressive iterative approximation method for computing offset surfaces, these three geometric adjustment algorithms involve changing offset distances, removing self-intersecting points, and interpolation. These algorithms have been successfully applied to five offset surfaces, including two cases of local self-intersections and global self-intersections. Experimental results demonstrate that these algorithms are able to compute rational, non-self-intersecting offset surfaces while limiting the number of control points to one to five times the number of the original surfaces. Furthermore, the offset surfaces computed using these algorithms have smaller errors compared to other existing algorithms, even when using the same number of control points.