Backes set an NHL-career high with seven goals and 14 points in 20 games during the 2016 Stanley Cup Playoffs. He helped the Blues reach the Western Conference Final for the first time since 2001. They lost in six games to the San Jose Sharks.
Brouwer, 30, had 18 goals in 82 games this season; he was the only Blues player to skate in every regular-season game. He had eight goals in 20 playoff games, including the winning goal in a 3-2 victory against the Chicago Blackhawks in Game 7 of the Western Conference First Round.
Brodziak, 32, scored seven goals in 76 regular-season games and had two goals in the playoffs. Upshall, 32, had six goals and 14 points in 70 regular-season games, and three points in 17 playoff games.
Ott, 33, has played for the Blues since 2013, when St. Louis acquired him and goalie Ryan Miller from the Buffalo Sabres for goalie Jaroslav Halak, forwards Chris Stewart and William Carrier, and two draft picks. Ott has 17 points in 122 games with the Blues.