Swaim caught one of two targets for eight yards in Thursday's 20-7 win over the Titans.
Swaim played only 21 snaps on offense (39 percent) while James O'Shaughnessy played 42 (78 percent) and caught a touchdown. The 2015 seventh-round pick appears to be operating as the clear No. 2 tight end in Jacksonville, and he isn't a notable factor in the team's passing game.