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Zidlicky's three-year extension is worth an average of $4 million per year, several sources told ESPN.com. Zidlicky's deal carries a partial or limited no-trade clause.
Stoner signed a two-year extension. Financial terms were not disclosed.
Both Zidlicky and Stoner were to be restricted free agents this summer. Zidlicky would almost certainly have been moved in advance of the March 3 trade deadline had the deal not been closed.
General manager Chuck Fletcher told ESPN.com on Tuesday that he wanted to keep Zidlicky in the fold but that he needed to get a deal done that day. It did.
Zidlicky, a member of the Czech Olympic team, has 36 points in 60 games this season for the Wild.
The 25-year-old Stoner has two assists in eight games. He is on injured reserve after hernia surgery.
Fletcher will likely continue to get calls on a number of his players who are scheduled to become unrestricted free agents, including veteran Owen Nolan and Eric Belanger.
Scott Burnside covers the NHL for ESPN.com. Information from The Associated Press was used in this report.