Bulman had a spell with Wycombe and Rhodes has spent time at Swindon
Oxford United have completed the double signing of Crawley midfielder Dannie Bulman and Rotherham winger Alex Rhodes on free transfers.
Bulman, 30, was out of contract with Town, who say Oxford's contract offer had "blown out of the water" the deal they offered - a claim United deny.
Rhodes, who the Millers have released, ended the season on loan at Woking.
The former Brentford and Bradford 27-year-old had a loan spell at Oxford's rivals Swindon in 2006.
Oxford manager Chris Wilder told the club website: "Dannie is someone who knows the league and is widely regarded as one of the best midfielders in it. He is a great character and exactly what we need in the middle of the park.
We certainly didn't blow anyone out of the water. Dannie's is a football decision not a financial decision
Oxford chairman Kelvin Thomas
"Alex will give us natural balance, pace, and options on the left. I have kept track of his career for the last two years and he is an exciting player to watch. He will give us that attacking width on the left."
Of the Bulman deal, U's chairman Kelvin Thomas said: "We certainly didn't blow anyone out of the water. Dannie's is a football decision not a financial decision.
"I firmly believe that Steve has to justify losing one of his best players to the fans. I understand that and we all know how the game works.
"As we have with all players we will offer something they are comfortable with but we're not breaking the bank for anyone. We have said that to agents and to players. Some agents come here and think we have a bundle of money, but that's not the case.
"The transfer fees we are talking about are not big fees. I know people are saying we have bid £150,000 for Scott Rendell but we haven't. We are not in that kind of ball park.
"Scott is a player that Chris (Wilder) and I have talked about, and we have put in a call to Peterborough but that sort of money is too rich for us. We were maybe looking for a potential loan but that was early on."
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