"We want something else. The only tool can't be the one tool we have. We need an additional tool in the toolbox," he said in an interview with CBC News.
White, a retired Mountie and former police chief, is making it clear that what he's supporting is not decriminalization.
"You still have the discretion to lay a criminal charge in the same format as before, process the narcotic in the same form as before and have someone appear in a court in the same form as before," he said.
Right now, police officers are supposed to lay criminal charges.
Under the Controlled Drugs and Substances Act in the Criminal Code of Canada, a person found guilty of possession of small amounts of marijuana could be jailed up to five years. A first-time offender could be fined up to $1,000 or face up to six months in jail.
Conservative MP David Wilks said officers often turn a blind eye, citing hours of paperwork and backlogged courts as reasons.
"If you decide to arrest that person for the joint, now you've removed yourself for two or three hours," said Wilks, who's also a retired police officer.
"So what do you do? You grab the joint and you just tell the kid, 'Don't do it again, and if you do it again, you're going to court' because you just don't have time."
When charges are laid, Wilks said the long and expensive court process usually results in no punishment. He said it has no consequence in the court system because possession of a small amount of marijuana is dealt with as a "minor crime."
More efficient than laying charges
At a meeting in Winnipeg last August, the Canadian Association of Chiefs of Police supported letting officers have the ability to ticket people found with 30 grams of marijuana or less. The association said it would be more efficient than laying charges.
At the time, Justice Minister Peter MacKay said he appreciated the chiefs' input but had no followup on their recommendation.
Now, the Conservative Party's law enforcement caucus is receptive to the idea.
"We think it's a positive move forward and we've expressed that to the powers that be," said Rick Norlock, caucus chair.
Norlock said both MacKay and Public Safety Minister Steven Blaney seem receptive to the idea.
But Norlock said the government would need to be careful in how it communicates any legislation.
"I guess the proviso would only be that we don't send out the message that we think possession of marijuana is a good thing and that's not something our party goes for."
Especially not after releasing attack ads against Liberal Leader Justin Trudeau, who came out in favour of legalizing marijuana last summer.
Trudeau also admitted to having smoked marijuana since being elected to the House of Commons, though he said he was "a very rare user."
Tories deal with reality, says legal expert
The Conservatives didn't miss an opportunity to criticize the Liberal leader, with MacKay calling it "a profound lack of judgment."
"By flouting the laws of Canada while holding elected office, he shows he is a poor example for all Canadians, particularly young ones. Justin Trudeau is simply not the kind of leader our country needs," MacKay had said in a statement.
A law professor at the University of Ottawa said it would be tough to keep up those attacks while changing the law on pot possession.
"The political pitfall, if you embrace a law and order agenda, is that it seems very close to decriminalizing the possession of marijuana, which the Conservatives are on the record as opposing," said Carissima Mathen.
"Strategically, it's actually not a bad choice because they are responding to reality. They're onside with the chiefs of police, with law enforcement who are telling them this is a reasonable, practical approach," she said.
"They do need to be careful, I think, in how they frame their continuing criticism of politicians who advocate a more dramatic change — actual decriminalization."
Still, Mathen said she was "pleasantly surprised" that there seems to be a push at all levels of the party to consider a ticketing system for marijuana offences.
"Frankly, it's refreshing to see, you know, consideration of less punitive measures to deal with what is an overburdened legal system and a crime that more and more Canadians feel is overbroad, is too harsh."
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