A wide range of agreement patterns found in Icelandic is problematic for any kind of grammatical theory. In particular, the agreement controller is selected according to case marking. To account for the complex interaction between case and agreement in the language, this paper proposes a new approach to agreement in Lexical-Functional Grammar (LFG). We replace the grammatical function specification of agreemenr controller in a lexical entry with two variables. The substitions of the variables are constrained independently in the grammar by utilising off-path constraints. The proposal neatly captures the complex agreement patterns that previously required a significant deviation from the standard theoretical assumptions (cf. Andrews 1982, 1990). Crucially, since the current approach is not designed as language-specific machinery, it can be a general theory of agreement in LFG.