Abstract Clause-elimination techniques that simplify formulas by removing redundant clauses play an important role in modern SAT solving. Among the types of redundant clauses, blocked clauses are particularly popular. For checking whether a clause C is blocked in a formula F, one only needs to consider the so-called resolution neighborhood of C, i.e., the set of clauses that can be resolved with C. Because of this, blocked clauses are referred to as being locally redundant. In this paper, we discuss powerful generalizations of blocked clauses that are still locally redundant, namely set-blocked clauses and super-blocked clauses. We furthermore present complexity results for deciding whether a clause is set-blocked or super-blocked