When it comes to Canadians' worst perceptions of the Senate, André Pratte is playing against type: he's begging for more work.

Pratte is one of the seven independent senators named by Prime Minister Justin Trudeau last April in a bid to make the institution less partisan.

One problem these new independent senators have encountered, however, is the limited budgets and representation on committees that stem from a system originally designed for two parties. The non-affiliated senators are now 34 per cent of the Senate – and are about to be 42 per cent - but have only 17 per cent of seats on committees, where most of the Senate's work is done, Pratte says.

"This shows for us the importance of changing the rules in the Senate so that independent senators play their full role," he said in an interview with CTV News.

Once Trudeau finishes filling the existing Senate vacancies - something that's reportedly happening within days - there will be 44 non-affiliated senators in a chamber of 105. The Senate Liberals, whom Trudeau liberated from caucus when the party was in opposition, have 21 seats. The Conservative Party has 40.

When Trudeau made the appointments last spring, the Conservatives and independent Liberals in the Senate rejigged slightly to allow the independents two seats on each committee. But it meant they had to give up their own seats - and that's the root of the problem, Pratte suggested.

"Rules are set up so political parties control the Senate. So we have to plead, really, for them to face reality that the Senate has changed and that independent senators are a large number and should have their proportional place in the Senate," he said.

Peter Harder, the self-styled government representative in the Senate, also noted the existing parties benefit from the current rules.

"The Conservatives, who have fewer seats after these appointments are made, in the Senate, than the independents, still have a majority on every committee of the Senate," he said.

But he noted the new appointments add momentum to the push to modernize Senate rules to allocate more money and committee seats to the independents.

"That work needs to be accelerated at a quicker pace than presently," Harder said.

Harder was named to the Senate by Trudeau to promote the government's agenda. The Senate Liberals have their own leader, Joseph Day, who said the independents can participate on committees - they just can't vote unless they're an official committee member.

"This is all for us to discuss in the Senate and I'll look forward to that debate," Day said. "If anybody feels that there should be more than [two independents per committee], then we'll sit down and talk about it."

Conservative Larry Smith said senators are already discussing what to do about independent slots on committees.

"As time moves on and the shift and balance change, those are all factors that will influence decisions that will be forthcoming," he said.

For Pratte, it's a simple matter.

"We think Canadians want the Senate to work fully, to be a modern institution, to be a less partisan institution, because this is what's at play... we think the rules could be changed right now so that independent senators can play the full role that they're appointed to play."

CORRECTION: This story has been changed to correct Peter Harder's role.