Abstract : This paper describes a generalization of the LowerUnits algorithm for the compression of propositional resolution proofs. The generalized algorithm, here called LowerUnivalents, is able to lower not only units but also subproofs of non-unit clauses, provided that they satisfy some additional conditions. This new algorithm is particularly suited to be combined with the RecyclePivotsWithIntersection algorithm. A formal proof that LowerUnivalents always compresses more than LowerUnits is shown, and both algorithms are empirically compared on thousands of proofs produced by the SMT-Solver veriT.