There has been controversy over the nature of so-called cognate objects in English, such as She died a natural death. Some claim that cognate objects are adjuncts (or adverbials), but others that they are arguments (or complements). There are also studies that treat some cases as arguments and others as adjuncts or something else. This leads to two related questions: what are cognate objects and how are they classified? This article argues for the complement analysis and proposes a cline of cognate objects with intransitive verbs, assuming a distinction between constructions and verb classes. The cline runs from idiomatic through productive types, the latter type of which further divides into argumental and nonargumental subtypes. Further notes are made on some advantages of the proposed analysis.