Arbitrator Stephen Burbank met with representatives of the league, players' union and the two teams on Thursday. The NFC East rivals were penalized for overloading contracts in the 2010 uncapped season despite league warnings. No ruling is expected soon.
The Redskins lost $36 million over two years and the Cowboys $10 million.
Burbank is a professor at the University of Pennsylvania.
Redskins general manager Bruce Allen says Washington's hearing lasted 2½ hours. He said, "We wanted to present our case and we were able to. ... We just have to let the process play out."