"It's a very unfortunate situation where you have a driver that has tested positive for using methamphetamines, and everybody agrees [such] people shouldn't be driving in NASCAR races," Boies summarised after the hearing.
A decision on the appeal is likely by April. A successful appeal would send the case back to US District Court for further litigation.
Mayfield's recent arrest for alleged possession of 1.5 grams of methamphetamine discovered after a police raid on his home following a tip-off about stolen property was not raised in the hearing.
"We're working our way through all that," Mayfield is quoted as telling reporters. "That will all come out pretty soon. We're trying to get to the bottom of everything."