Catmull-Clark subdivision scheme provides a powerful method for building smooth and complex surfaces. But the number of faces in the uniformly refined meshes increases sharply with respect to subdivision depth. This paper presents an adaptive subdivision technique as a solution to this problem. Instead of subdivision depths of mesh faces, the adaptive subdivision process is driven by labels of mesh vertices, which can be viewed as subdivision depths of the surface in the vicinity of the mesh vertices. Smooth transition between faces with different subdivision depths is provided by an unbalanced-subdivision process. The resulting meshes are crack-free, and all the faces are quadrilaterals. Limit surface of the resulting meshes is the same as the original limit surface. Test results show that the number of faces generated in the adaptively refined meshes is one order less than the uniform approach. The proposed technique works for cubic Doo-Sabin subdivision surfaces, non-uniform cubic subdivision surfaces and combined subdivision surfaces as well.