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Barry, who is tied with Frank Lampard in second on the all-time top Premier League appearance list, has extended his deal until 2018.
Meanwhile, Baines is now tied to them until 2019 while Holgate’s four-and-a-half-year agreement takes him to 2021.
And Koeman - who recently expressed the desire to revamp his squad - is thrilled to have the futures of three key members of the club secured.
He told the club’s website: “With Leighton, his attitude is always perfect. He likes to work hard, he likes to learn, he is a technical player with a good view of the game and I’m really happy to have him in the team this season and also for the longer term.
“Offensively, he’s a strong player who can cross the ball well and he has that cleverness in the game and in the moment, a quality that’s not in every player.
“He’s one of the experienced players in our team and what you like to have in your team is a balance in ages in the group. Players like Leighton, Phil Jagielka and Gareth Barry are leaders in our dressing room and on the pitch.
“Mason is one of the big talents at the club. Of course, he started playing this season and did a great job. He can play out of different positions in the team defensively.
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“He was really comfortable when he got his chance in the team. He showed strengths with the football and strengths in defending. He’s the future for the club and other young players like him.”
Barry is 23 appearances behind Ryan Giggs’ Premier League record, with the new deal making him highly likely to break that mark.
“Like Leighton, Gareth Barry is a clever player on the pitch,” added Koeman.
“Only Ryan Giggs has played more games in the Premier League and let’s hope he will smash every record. He’s a quiet person but a strong character. He knows what he can and can’t do.
“He is a key player for the team. Of course, sometimes you need to protect older players, with all due respect. Gareth is 35 but he is still so important for the team and I’m very happy he has extended his contract.”
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Barry hailed Koeman after signing the deal, crediting the Dutchman with giving him fresh motivation.
“The new manager has come in and given me a new lease of life,” the midfielder said.
“It’s someone else to try and impress and new tactics to take on board. It’s really helped my game and I’m looking forward to taking that on and enjoying this season, which is hopefully a successful one.
“They say you can’t buy experience and, for me, it feels so much easier going out on the pitch knowing what I know.
“Obviously there’s different sides of the game that are needed, such as energy, but I feel as comfortable on the pitch as I have ever done and a successful team here is something I want to be part of.”
