The Red Sox handled some offseason business Thursday by agreeing to a one-year, $800,000 contract with righty Cooper Criswell, according to a source.

Criswell is a pre-arbitration player so he was not a free agent and would be under club control even if an agreement wasn’t reached . After making $1 million in each of the last two seasons, he’s taking a small pay cut to remain on the 40-man roster. The new deal prevents him from being a non-tender candidate later this month.

Criswell’s new deal came before a Thursday deadline for teams to clean up their 40-man rosters by reinstating players who ended the regular season on the 60-day injured list. Boston needed to clear one spot and did so by designating reliever Luis Guerrero for assignment. The timing of Criswell’s new agreement is in

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