OTTAWA -- The need for -- and even the name of -- a new Conservative bill aimed at barring polygamous and forced marriages came under fire Thursday in the Senate.

Bill S-7, entitled the "Zero Tolerance for Barbaric Cultural Practices Act," amends immigration and criminal laws with the aim of keeping polygamists out of Canada and preventing women and girls from being married against their will.

"We wish we could say in the Canada of 2014 that these were no longer challenges for us domestically," Immigration Minister Chris Alexander told the Senate human rights committee.

"But as we know from communities across the country and from the daily fact of violence against women, there remain challenges and we remain duty-bound to act against them."

Conservative Sen. Raynell Andreychuk raised concerns, however, that the government's stated goal of combating violence risks being overshadowed by the bill's dramatic title.

"In that title, if you wanted 'barbaric cultural practices' -- which probably wasn't going to be my choice -- but if you wanted that, I wished you had added something like 'violence' in there," Andreychuk said.

Alexander defended the name. The fact it has already generated debate means it's already doing its job, he argued.

"What is a barbaric practice? It is a practice that is unacceptable; it is a practice that involves violence that is in many respects indiscriminate, gratuitously meted out, behind closed doors, where women and girls are defenceless, whereby whole families conspire to ensure underage women lie about their age, take part in a forced marriage," he said.

"It is -- in my view, and I think in the view of many Canadians -- barbaric to subject your family members to that kind of abuse."

Andreychuk later said if the government does believe violence against women is addressed by the title of the bill, she is satisfied with it.

The new law would deny entry to Canada to those seeking to practice polygamy, which is illegal in this country.

It would also require "free and enlightened consent to marriage" and sets a federal minimum age for marriage at 16 -- a threshold that wasn't already enshrined in law.

It also makes it an offence for anyone younger than that to be taken out of Canada to be married elsewhere.

That's a direct reference to the polygamous community of Bountiful, B.C., where it's long been believed that teenage girls are shuttled back and forth to the U.S. for marriage.

Four members of that community are currently facing charges in relation to that practice under existing Canadian laws, but past attempts to obtain a polygamy conviction in Bountiful have failed.

The bill also seeks to clarify what it means to be provoked into committing a crime.

That change seeks to remove the provocation option as a defence in cases that involve so-called "honour killings," though immigration officials acknowledged no one has ever tried to use it before.

"The law you bring here has very little evidence based to it," Liberal Sen. Art Eggleton told Alexander. "We've heard of one case of forced marriage that this is based on, and absolutely no successful cases of honour killing."

"You have current laws to deal with it, and you seem more focused on trying to bring a new law in when you have existing laws you could (use to) deal with these matters."

Alexander said extensive research has been done on the issue of forced marriages in Canada, noting in particular the work of the South Asian Legal Clinic of Ontario.

In a 2013 survey of social assistance agencies in Ontario and Quebec, the agency uncovered 69 forced marriage cases in 2010, 64 cases in 2011 and 77 cases in 2012.

The organization itself opposes the proposed bill.

Deepa Mattoo, the clinic's executive director, is set to testify before the Senate committee next week.

She said it appears that while the minister read her research, he doesn't seem to have read the conclusions.

"There was a clear-cut recommendation put forward and it very clearly said: please do not criminalize forced marriage," she said.

Criminalization does not help women who are victims, she said. Had her group been meaningfully consulted on the language of the bill, they could have helped draft something that would address the problem, she added.

"This whole process seems like lip service," she said. "It's not really giving real, tangible tools which women need."