In this paper, we argue that an adequate description of Moksha Mordvin complement clauses requires preserving the traditional LFG distinction between OBJ and COMP grammatical functions. Most clausal complements in Moksha belong to one of the two major types: clauses headed by deverbal nouns (nominalizations) and finite complement clauses introduced by complementizers. The behaviour of nominalized clauses mostly corresponds to the behaviour of nominal arguments, such that they can be distributed between the grammatical functions SUBJ, OBJ, and OBL, without the need for an extra COMP function. Similarly, the majority of finite complements can be viewed as SUBJ, OBJ and OBL depending on the case form of their proforms and quantificational modifiers and the presence of object agreement on the verb. However, a subset of verbs does not fit into this classification: on the one hand, their complements do not trigger object agreement; on the other hand, they cannot be viewed as SUBJ or OBJ, because they cannot be replaced by nominal proforms and cannot be accompanied by any quantificational modifiers. We conclude that an additional grammatical function COMP must be used to account for the behaviour of these complement clauses.