The Twins filled out their starting rotation Tuesday.

Sort of.

Signing veteran pitchers Homer Bailey and Rich Hill gives the Twins an experienced five-man rotation of Jose Berrios, Jake Odorizzi, Bailey, Hill and Michael Pineda.

But neither Hill, who is coming off elbow surgery, nor Pineda, who is serving 39 more games of his 60-game suspension for using a banned diuretic, will be available until late May or June.

And the Twins have only four off-days from the time the season starts on March 28 until May 4, so rookie-level pitchers like Devin Smeltzer, Randy Dobnak and Lewis Thorpe will likely be counted on to start for a team trying to defend its American League Central title.

At any rate, the Twins’ 40-man roster is now full after Bailey and Hill got one-year contracts.

The 33-year-old Bailey is a 13-year major league veteran who split last season between Kansas City and Oakland, going 13-9 with a 4.57 ERA in 31 starts. In 243 major league games, all starts, the righthander is 80-86 with a 4.57 ERA. He was the seventh overall choice in the 2004 draft out of La Grange (Texas) High School.

His contract will be worth $7 million, with incentives if he reaches 180 innings.

Bailey’s best season came in 2013 when he was 11-12 with a 3.49 ERA for the Reds and had 199 strikeouts in 209 innings. Cincinnati gave him a six-year, $105 million contract extension at that point, but he had arm trouble in 2014 and had Tommy John surgery in 2015. More arm surgery followed; in 2018 he was 1-14 with a 6.09 ERA and the Reds traded him in a salary dump to the Dodgers, who released him.

After signing a minor league deal with Kansas City, Bailey was 7-6 for the Royals last season. They traded him to the A’s at the deadline, and he was 6-3 for a playoff team. He has averaged 7.4 strikeouts per nine innings over his career, with a four-seam 95 mph fastball his “out” pitch; he will be a nice project for Twins pitching coach Wes Johnson.

Hill, a lefthander, will be 40 on Opening Day, at which time he is likely to be on the 60-day injured list. He has pitched for eight teams in 15 seasons, and had only 13 starts for the Dodgers last season because of portion of the UCL in his left elbow detached. He had surgery in October and will be out until at least June. Hill was 4-1 with a 2.45 ERA and 72 strikeouts in 48⅔ innings last season.

His contract is for $3 million, with incentives worth close to $10 million.

In 2013, Hill made 63 appearances in relief for the Cleveland, but shortly thereafter turned his career around by adding a devastating curveball. The major problem with throwing his curve is that it tears the skin on the side of his middle finger, and that has limited him, although he made 25 starts in both 2017 and 2018 for the Dodgers’ World Series teams.

He has also pitched for the Red Sox, Cubs, A’s, Angels, Yankees and Orioles.

In 3½ seasons in Los Angeles, Hill started 68 games and had a 3.16 ERA and a 7.1 WAR. In 50 innings in the playoffs, his ERA was 2.70; his last contract with the Dodgers was for three years and $48 million.

Hill and his wife made headlines on Dec. 22 when they were detained by police at an NFL game between Buffalo and New England in Foxborough, Mass.

Caitlin Hill repeatedly tried to enter Gillette Stadium with an oversized bag, and as police took her into custody, Rich Hill was also arrested because he tried to stop them. On Dec. 23, they both were ordered to pay $500 fines for civil infractions. Hill released a statement where he said, “Seeing my wife handcuffed for a problem that started because of her fanny pack was extremely difficult for me to witness. This was all overblown and we are glad to have it behind us.”

Smeltzer, a lefthander, started six games for the Twins, and had a 3.86 ERA in 11 overall appearances. Dobnak, a righthander who started the season in Class A, was very impressive, with a 1.59 ERA in 28.1 innings, but got a start in the playoff series against the Yankees and gave up four runs in two innings. Thorpe, another lefty who started 19 games at Class AAA Rochester, appeared in 12 games for the Twins, with two starts, and had a 6.18 ERA.

Two major league sources confirmed the Twins, who non-tendered starting first baseman C.J. Cron, are still very much in the mix for free agent third baseman Josh Donaldson. If Donaldson signs, the team would likely move third baseman Miguel Sano to first after Cron signed a free-agent contract with Detroit.