The Twins opened space on their roster Tuesday by opening space in their bullpen, but they made sure to keep their most valuable setup men.

Righthander Tyler Duffey and lefty Caleb Thielbar, each of whom who pitched more relief innings than any Twin but the now-departed Alex Colome, agreed to one-year contracts on Tuesday. Duffey is set to earn $3.8 million in 2022 and Thielbar $1.3 million.

Righthander Jharel Cotton, claimed off waivers from the Rangers earlier this month, settled for a $700,000 salary, or roughly $150,000 more than the major-league minimum.

But the Twins chose not to offer contracts to righthander Juan Minaya and lefthander Danny Coulombe, making them free agents. The pair appeared in 29 games apiece in middle-inning roles last season, each posting respectable ERAs — 2.48 for Minaya and 3.67 for Coulombe — and could still be signed later.

All-Star reliever Taylor Rogers, catcher Mitch Garver and infielder Luis Arraez were each offered contracts by Tuesday's 7 p.m. deadline, keeping them on the roster and allowing them to file for salary arbitration if they can't come to an agreement otherwise.

Meanwhile another promising reliever came and went in the span of about eight hours Tuesday, but he remains likely to become a Twin at some point in 2022. Trevor Megill, a hard-throwing right-handed reliever who debuted for the Cubs in 2021, was claimed off waivers by the Twins on Tuesday morning, but was not offered a major-league contract and technically became a free agent that evening.

Why the hello-goodbye? It's a maneuver teams can use to send a player to the minor leagues without passing him through waivers, which is otherwise required during the offseason. During his brief time on the 40-man roster, the Twins could have negotiated a minor-league contract, likely with a higher salary than a normal Class AAA deal, in order to keep him in the organization. If he didn't, Megill — whose fastball averaged 96.3 mph during his rookie season and helped him rack up 30 strikeouts in 23 2/3 innings in four separate stints with the Cubs in 2021 — also is a free agent. The Twins declined to comment on his status.

Either way, Megill's short stay cost Jake Cave his roster spot, perhaps permanently. To make room for the newcomer, Cave was assigned outright to Class AAA St. Paul. Cave signed a one-year contract for $800,000 earlier this month, keeping him in the organization as outfield depth.

Acquired in a spring 2018 trade with the Yankees, Cave has spent four seasons as the Twins' fourth outfielder, but his 2021 season (a .189 average and .541 on-base-plus-slugging percentage) was his worst. The Twins decided to keep the 28-year-old Virginian, though their signing of Byron Buxton to a long-term contract this week makes Cave far less likely to make the team next spring.

The Twins' 40-man roster now has three vacancies, and might for a while, with baseball apparently headed for a lockout Thursday.