In this paper, we improve a result of Seetapun and prove that above any nonzero, incomplete recursively enumerable degree a, there is a high2 r.e. degree c>ac>a witnessing that a is locally noncappable . Theorem 1.1 provides a scheme of obtaining high2 nonboundings , as all known high2 nonboundings, such as high2 degrees bounding no minimal pairs, high2 plus-cuppings, etc.