The policy was toughened for this season, and a first-time offense will result in suspension.
"This isn't a first-time offense," he said.
Under the minor league policy, players receive a 15-game ban for a first-time offense, followed by bans of 30 games, 60 games and one year.
Under the old policy, which was established in 2002, a first-time offense would only result in treatment for the player, and the player would not be named.
He also said it did not go far enough to guarantee incarceration, including for some first-time offenses involving "nonsensical violence," like purse snatching.
If a player was caught using steroids during training camp or some other off-season workout, they were suspended for 30 days for a first-time offense.
More precise monitoring and tracking may also prompt the authorities to release some prisoners earlier, or even eliminate prison sentences for some first-time offenses.
Mr. Draper, said he thought a first-time offense should be a fine, with subsequent offenses including jail.
A first-time offense carries a three-month ban from competition.
Possession is currently an unclassified misdemeanor punishable by 30 days in jail and a $500 fine for a first-time offense.