The next season saw Swift continue to be a regular player in European competition, but feature less prominently in the league. He made 15 appearances in the 2005–06 Celtic League, but over half of these came as a replacement. Connacht finished the season level on points with last-placed Glasgow Warriors. Meanwhile, the 2005–06 Challenge Cup saw change's to the competition structure, with the addition of pool stages followed by single-leg knockout games. Connacht finished second in their group to Worcester Warriors, with Swift featuring in four of the team's six games. This was enough to see the team through to the quarter-finals, where they faced Newcastle Falcons. Swift was used as a replacement against Newcastle, but he was sin-binned during the match as Connacht crashed out.