Summary: The authors introduce a new class of operators that are weakly decomposable relative to the identity, and some of their properties are derived; for example, these operators have the single valued extension property. The main result is that every generalized intertwining of an operator having property \((\delta)\) with such a weakly decomposable one is necessarily bounded whenever certain side conditions are satisfied. Examples also show that this class of weakly decomposable operators is not comparable by inclusion to the classical cases (e.g. decomposable operators).