The Avalanche sent Calgary a second-round pick in 2014 for Berra. The Swiss rookie made 29 appearances for the Flames this season, posting a 9-17-2 record with a 2.95 goals-against average and a .897 save percentage.
Berra was selected in the fourth round, 106th overall, by St. Louis in the 2006 NHL draft.
The Flames then acquired a third-round pick in 2014 for Stempniak. The American veteran had eight goals and 15 assists in 52 games this season.
Stempniak has played 616 career games with St. Louis, Toronto, Phoenix and Calgary, scoring 146 goals and adding 184 assists along with 220 penalty minutes.