This paper presents an f-command based analysis of non-reflexive (possessive) Warlpiri binding. Simpson (1991) provides a c-command based analysis of a set of non-reflexive binding data, and explains binding differences between English and Warlpiri binding data by a difference in structure, proposing a flat structure for Warlpiri and a hierarchical structure for English. I assume a more hierarchical structure for Warlpiri along the lines of Simpson (2007) and illustrate that an f-command based approach using lexical specification of binding constraints as proposed by Dalrymple (1993) is better capable of accounting for the Walrpiri binding data. Not only does a hierarchical structure for Walrpiri not allow for a c-command based approach, but a level of variation in the binding data in Warlpiri illustrates that lexical specification of binding constraints for different dialects/individual speakers is necessary to account for the data. For the specific variety of non-reflexive binding data described by Simpson (1991) I propose an analysis only taking f-command into account (and not the grammatical function hierarchy or f-precedence), which is a novel way of accounting for binding data.