"We took the opportunity to review the test results and present Bryan's physicians' records and testimony demonstrating that they authorized Bryan to take weight loss medication," Pittman's lawyer David Cornwell said in an e-mail to The Associated Press.
Bumetanide is banned under the NFL steroids policy because it is considered a masking agent for steroids. However, Cornwell's statement continued: "Bryan is also gratified that the evidence confirmed that he did not take steroids."
Texans coach Gary Kubiak said Pittman went directly from Houston's game in Minnesota Sunday to New York for the hearing.
"It's our understanding that we will know something [Tuesday]," Kubiak said. "We have not heard back from them today."
According to the NFL's policy, the first positive test results in a four-game suspension.
Pittman is one of six to eight players allegedly under investigation for taking Bumetanide.
Saints players Jamar Nesbit and Deuce McAllister have said they tested positive for the drug after using an over-the-counter weight-loss pill called StarCaps. The makers of StarCaps suspended shipments of the product last week after accusations it contains the banned substance, but does not list it as an ingredient.
Nesbit, who has already served a four-game suspension, filed suit against StarCaps last week.
Minnesota defensive tackles Pat Williams and Kevin Williams have been identified in various reports as players who have allegedly tested positive for the drug. Pat Williams said he isn't concerned about when he will hear about a possible punishment and is preparing to play the last eight games of the schedule.
"Everything will be good," he said. "I ain't worried about it."
He hasn't admitted to testing positive, though he hasn't denied the charge, either.
"I don't know nothing ... [Coach Brad Childress] just told me to play," he said. "Whatever goes down, I'll tell you all."