The Texans submitted a $2.025 million original round restricted free agent tender for defensive lineman Brandon Dunn.
Dunn started a career-high 10 games last season, recording 24 tackles, four for losses, one forced fumble and an interception.
And the AFC South champions re-signed wide receiver DeAndre Carter to a one-year contract.
BRIAN T. SMITH: Optimistic about future for Texans
Carter caught 20 passes for 195 yards. He averaged 9.1 yards per punt return and 24.6 yards per kickoff return in seven games after being claimed off waivers from the Philadelphia Eagles as the replacement for kick returner Tyler Ervin.