Automatic term identification and investigating the understandability of terms in a specialized domain are often treated as two separate lines of research. We propose a combined approach for this matter, by defining fine-grained classes of termhood and framing a classification task. The classes reflect tiers of a term’s association to a domain. The new setup is applied to German closed compounds as term candidates in the domain of cooking. For the prediction of the classes, we compare several neural network architectures and also take salient information about the compounds’ components into account. We show that applying a similar class distinction to the compounds’ components and propagating this information within the network improves the compound class prediction results.