The Scandinavian languages are very closely related but also vary syntactically in interesting ways, making this family useful in the study of typology variation. In this paper the issue of non-local reflexives, or ‘long-distance reflexives’ (LDR) is investigated. New LDR data from the Scandinavian languages is presented to show that the Binding Conditions cannot account for the variation in LDR in these languages, since the range of domains that LDR may or may not occur in in each variety varies non-hierarchically. For instance, LDR in Icelandic may be bound out of a finite complement clause but not out of a relative clause, while the reverse is true in most Norwegian dialects. Faroese allows LDR out of both clause types, but many dialects do not allow a second person pronoun to co-occur in a sentence containing LDR, which does not generally affect Icelandic or Norwegian LDR. An extension of Dalrymple's (1993) typology of anaphora, which is set within the framework of Lexical-Functional Grammar, can account for this data, using a combination of inside-out and outside-in functional uncertainty equations, on- and off-path constraints and positive and negative constraints, all of which refer to elements (potentially) found in functional-structure.