The status of 'indirect objects' in Estonian has long been a matter of controversy. One approach (Kure 1959, Klaas 1988, Nemvalts 2004) recognizes a class of 'indirect objects', which represent indirectly affected participants. Another approach (Vääri 1959, Erelt 1989, 2004, Erelt et al. 1993) disputes the usefulness of this distinction, and assigns all grammatical dependents other than subjects and direct objects to a large and heterogeneous class of 'adverbials', based on the fact that indirect dependents are similar in form to adverbial modifiers. The present paper takes up this traditional issue from a theoretical perspective, and argues that Lexical Mapping Theory (Bresnan & Zaenen 1990) clarifies a basic syntactic contrast between oblique functions (the 'object' or 'governed' adverbials in current Estonian grammar) and ungoverned adverbial modifiers. The general dissociation between form and function in LFG clarifies how a single semantic case form can function syntactically either as a modifying adverbial or as a governed oblique function.