If Medlock, a fifth-round pick out of UCLA, had not been signed, it could have created a bad situation. He was already handed Kansas City's place kicking job when Lawrence Tynes got traded in May.
"This means that every one of our draftees is in camp but one," Peterson said as the Chiefs prepared for their first practice.
Johnson, who is still under contract, is demanding compensation in the range of $28 million guaranteed, insisting he be paid as much as San Diego Pro Bowler LaDainian Tomlinson.
But he will be fined more than $14,000 for every day he misses, and Peterson signaled a tough stance by the Chiefs.
"We continue to talk," Peterson said. "But we are a long way apart."
The Chiefs point out that Tomlinson, unlike Johnson, is an accomplished blocker as well as a dangerous pass receiver.
"Larry is a terrific back. But I don't put him in the LaDainian Tomlinson category," Peterson said. "Hopefully, he can get there, becoming a more complete back like LaDainian. This guy wants money beyond LaDainian Tomlinson. That's not going to happen with us."
Peterson said he is determined to be optimistic.
"The one player is without a contract, Dwayne Bowe, so he doesn't have to be here. The other player, Larry Johnson, does have a contract for 2007 and he is supposed to be here," he said. "I'm sure the question will be asked, and it is affirmative. We are going to be fining Larry $14,223 or whatever the amount is (by NFL rules) for every day he's not here.
"I am personally still optimistic that we will get something done with both these players. I would like to get something done quickly, obviously, but sometimes it takes time. I've been through this before with a lot of players. Right now specific to No. 1 draft choices, there are still a lot of them out. The encouraging thing is there are No. 1's making deals now and we'll continue to work at that with Dwayne's agents."
Johnson's situation could be affected by the unexpected return of three-time Pro Bowl running back Priest Holmes, who has been out of football since sustaining head and neck trauma in October 2005. The Chiefs are not counting on Holmes to be the featured back - he will turn 34 early in the season - but they are hopeful he can get about 12 touches every game.
While Holmes' presence might put pressure on Johnson to get into camp, Peterson denied reports that Johnson was drafted in 2003 partly because Holmes was involved in a contract dispute. Holmes, who also was coming off hip surgery at the time, had said he wanted a contract extension but a deal was worked out peacefully and without acrimony, Peterson said.
"I guess I have a terrible relationship with the media. Every contract must be a `dispute,"' Peterson said. "The fact is, Priest and his agent, Todd France, have always had a very good relationship with the Chiefs. I find Todd France one of the easiest guys to negotiate with."
Peterson also scoffed at speculation that Holmes was being used as a pawn in the Johnson negotiations.
"Anybody who knew Priest would throw that one away," he said. "Priest does what he wants to do. He is his own man. There's no way in the world I could talk him into coming out just as a ruse, as a way to create leverage on Larry. We've already talked to Priest about what his role would be if he does make it. He's going to take 12 to 15 snaps a game, and that's it.
"He will be in a physically-unable-to-perform status as about three or four of other players are. We want to bring him along slowly, make sure he doesn't get hurt, and gauge where he is with his football conditioning."
The Chiefs also said Friday they had agreed to terms of two-year contracts with free agent cornerback Will Poole and defensive tackle Patrice Majondo-Mwamba. They received a national player exemption for Majondo-Mwamba, a native of the Republic of the Congo, which means the club can carry 88 players on the current training camp roster.