Recent research has shown that labeling ontologies can be useful for restricting the access to some of the axioms and their implicit consequences. However, the labeling of the axioms is an error-prone and highly sensible task. In previous work we have shown how to correct the access restrictions if the security administrator knows the precise access level that a consequence must receive, and axioms are relabeled to that same access level. In this paper, we look at a more general situation in which access rights can be granted or denied to some specific users, without having to fully specify the precise access level. We also allow a more flexible labeling function, where the new access level of the relabeled axioms may differ from the level of the restriction. We provide black-box algorithms for computing suggestions of axioms to be relabeled.