In the 2006–07 Celtic League Swift featured in 14 of the team's 20 games, starting in four of them as Connacht finished above only Border Reivers, a team that was disbanded at the end of the season. Swift also played in four 2006–07 European Challenge Cup matches. He started in each of these games, playing Montpellier twice, before facing Bath and Harlequins, but couldn't prevent Connacht being eliminated at the pool stages. The game against Montpellier was Swift's hundredth appearance for Connacht, making the fifth player to reach the milestone for the province. With the number of competing teams reduced to ten for the 2007–08 Celtic League Swift featured in 12 games for the province, starting all but two of these, as Connacht finished bottom of the table. Swift also started in all six of Connacht's 2007–08 Challenge Cup games, playing at home and away against Brive, El Salvador and Newcastle Falcons, scoring a try against El Salvador. Connacht finished third in the group and were eliminated.