The role of self-functions in TRIZ is rather ambivalent. Whereas the typical standard approach in Function Analysis regularly prevents them from even being identified, self-functions prominently appear in trimming techniques, are explicitly proposed in an Inventive Principle, and get involved in considerations about systems of ultimate ideality as well. This work points out some misunderstandings and inconsistencies in the standard perspective, elaborates the actual nature of self-functions and clarifies the relation to practical application. In addition, different trimming variants are shown to result in systems getting either cheaper or better, depending on the type of the trimmed function.