This paper is a first report on an ongoing project aiming at building up a database of non-canonical argument marking in Lithuanian in contrast to other languages with relatively rich systems of morphological cases. The language with which we begin the comparison is Icelandic. The overarching aim consists not only in a unified inventorisation of relevant units, but in disclosing (i) regularities in the alternation of coding patterns and (ii) the factors underlying such variation. We will concentrate on case marking; this however implies agreement patterns as well, insofar as in these two languages only nominatival NPs trigger agreement on the finite verb (= predicate of the clause). We further concentrate on verbs with non-canonical marking of their highest-ranking argument (HRA); the notion of HRA is defined on the basis of the Actor-Undergoer Hierarchy as developed in Role & Reference Grammar (see 2.1). What we present here is not yet a comprehensive description of the whole body of data, but rather a problem paper which details some conceptual issues and highlights some prominent types of argument coding and their relation to lexical groups.