The aim of this paper is to analyse the grammatical status of independent complement constructions in Swedish and Danish, i.e. constructions introduced by the complementizer att or at but without an accompanying main clause. These constructions can be used with two main functions: to express the speaker’s evaluation of a presupposed state of affairs, or to elaborate on an aspect of the preceding discourse. In recent literature on these and similar constructions in other languages, both types have been analysed as instances of the category of insubordination (Evans 2007), i.e. constructions that combine subordinate marking with main clause use. We will argue that this analysis works well for the 'expressive' type, but that it cannot account for some of the typical properties of the 'elaborative' constructions, like the fact that they are pragmatically dependent and inconsistent in their use of subordinate marking. As an alternative, we will show that elaborative constructions can be dealt with much more naturally in terms of an existing model of dependency shift in clause combining, like the subordinate-coordinate shifts observed for many other types of subordinators.