The first arbitration hearing took place on Wednesday in New York City, lasted more than two hours and concluded without arbitrator Shyam Das ruling.
According to reports from NFL.com, no further hearings in this particular grievance has been scheduled. (For more on the differences between the grievances, check out CBSSports.com's interview with NFLPA lawyer Jeffrey Kessler here.)
Kessler argued for the NFLPA, while NFL outside counsel Dan Nash handled the arguments for the league.
Das, per the Associated Press, has not determined or said when he would rule.
Anthony Hargrove (now of the Packers) and Scott Fujita (now with the Browns) attended the arbitration hearing. Will Smith and Jonathan Vilma (both still with the Saints) did not attend the hearing.
There is a separate arbitration hearing scheduled for May 30 in New York City relating to the second grievance filed by the union.