The construction of a GC 1 cubic interpolating curve that lies on the same side of agiven straight line as the data points is studied. The main task is to choose appropriate approachesto modify tangent vectors at the data points for the desired curve. Three types of approaches forchanging the magnitudes of the tangent vectors are presented. The first-type approach nodifiesthe tangent vectors by applying a constraint to the curve segment. The second one does the workby optimization techniques. The third one is a modification of the existing method. Three criteriaare presented to compare the three types of approaches with the existing method. The experimentsthat test the effectiveness of the approaches are included.