Both players were vying for roster spots on partially guaranteed deals after strong showings with the Celtics' summer league teams in Orlando and Las Vegas, but neither did enough in camp and exhibition play to nail down a spot.
The Celtics will eat roughly $250,000 in guaranteed money, including $236,800 for Christmas, whose minimum deal was half-guaranteed.
Celtics coach Doc Rivers chalked up the decision to there not being enough spots on the 15-man roster.
"Two good kids, both played hard," Rivers said. "Just really came down to numbers, and we just didn't have enough room."
The moves could indicate that rookie second-round draft pick Kris Joseph, playing on a fully non-guaranteed deal, is closer to securing a spot, but Boston also might be pondering adding a veteran ball-handler for one of its final roster spots.
While $250,000 doesn't sound like much to absorb for a team with a payroll of nearly $72 million, Boston is hard-capped at the $74.3 million tax apron after using the full value of its mid-level exception on Jason Terry, leaving every dollar valuable while trying to construct the deepest 15-man roster possible.
Rivers said the team still plans to keep 15 players and is open to adding someone from the outside if a cheap veteran can help this team at any position, not just a backup ball-handler.
"Maybe the Heat will cut LeBron (James) or whoever," he said. "We're always looking. Every team is always looking. If nothing comes, does that bother us? No. It'd be great to get another guy at any position. Obviously, at (point guard) it would help, but we can't also forget that Avery (Bradley) is coming back too. We don't want to overdo the point guard thing."
Rivers did caution that the moves are in no way a reflection that Bradley is moving closer to a return. He also said the long-term potential of Joseph separated him from Christmas and Smith at this point.