Baker and Mruczkowski were restricted free agents, and Mays and Wright were exclusive-rights free agents.
The 25-year-old Wright first signed with the Patriots as an undrafted free agent out of the University of Cincinnati in 2005. The 6-foot-4, 295-pounder has played in 29 games, making four starts in two seasons with the team.
Mruczkowski, 26, originally signed with the Patriots in 2003 as an undrafted rookie free agent out of Purdue. The reserve lineman has played in 18 games.
Mays, 23, originally was signed as an undrafted rookie free agent out of Notre Dame last spring. He has played primarily on special teams.
Baker, 24, was claimed off waivers from Minnesota in November and played in three games for the Patriots.
The team did not disclose terms of the contracts.
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