Arnold and Sadler (2010) provides a `Pottsian' analysis of supplemental constructions, in particular appositive (non-restrictive) relative clauses, in the framework of LFG and glue semantics. The account utilizes an inference rule that splits single glue resources into their `at-issue' and supplemental sub-parts, and introduces other resources that re-integrate the at-issue and supplemental content, so that the supplemental content gets `widest' scope, rather than (as in Potts' account) being scopeless. No proper justification is given for either of these aspects of the analysis. This paper shows that while the splitting rule is unnecessary, apparatus for re-integration is essential. The resulting treatment is both better justified, and formally cleaner.