Ed Miliband wants 'more serious' PMQs
Labour wants a "more serious tone" to Prime Minister's Questions, the BBC understands, amid concerns the weekly session had got "out of control".
Wednesday's clash was quieter and more consensual than in recent months.
The BBC's Nick Robinson said the subdued atmosphere was partly due to the death of Labour's Paul Goggins.
But he said there were concerns among Ed Miliband's team that the encounter had become a "shouting match" with MPs unable to hear what was going on.
Prime Minister's Questions, where the prime minister faces questions from his opposition counterpart and backbenchers for about half an hour, is the highlight of the parliamentary week.
But critics say the frequent barracking by MPs of speakers from other parties makes for an undignified spectacle and turns off the public.
Successive prime ministers have also been accused of not answering questions properly.
When he became Conservative leader in 2005, David Cameron said he wanted to get away from "Punch and Judy" knockabout during the session but admitted three years later he had not succeeded.
In recent months, Prime Minister's Questions - commonly known as PMQs - has become particularly rowdy, with Mr Cameron frequently taunting Labour leader Mr Miliband over his union links and clashing with the shadow chancellor Ed Balls, describing the latter last month as a "turkey".
The BBC's political editor said the very different mood in the Commons on Wednesday could be partly explained by the fact that many MPs had only heard about the death of former minister Mr Goggins - who was widely respected across the House - just before the session began.
But he said that it was notable that the Labour leader had asked questions about the recent floods and problem gambling rather than more politically divisive subjects such as the economy or spending cuts and had also refrained from making a joke about David Cameron's hairdresser getting an OBE.
"Before Christmas I know Ed Miliband was beginning to believe that Prime Minister's Questions had got out of control and it was a shouting match," he told the BBC's Daily Politics.
"Ed Miliband took the view something needed to change."
Noise levels in the chamber in recent months meant journalists following proceedings in the Commons gallery could "scarcely hear a single word", he added, while MPs had had to lean backwards to listen to the speakers in their seats.
In the early 1990s, Nick Robinson said, the then Labour leader Neil Kinnock had approached Prime Minister John Major to seek support for changing the tone of PMQs and the two sides had "agreed to disarm" for a few weeks.
But the BBC's political editor added he had "no evidence" that the Conservatives and Labour had had similar discussions this time around.
Shadow business secretary Chuka Umunna told Daily Politics that politicians and the media needed to reflect on the purpose of PMQs and the impression the spectacle gave to the public.
While a low-key session might not make such "good television", he said, it was often more appropriate for scrutinising the government and addressing important issues such as foreign policy.
"It does not always have to be a massive knockabout," he said.
Treasury Minister Sajid Javid said he believed Mr Goggins's death was largely responsible for the "sombre attitude" and Wednesday's encounter would not necessarily set the tone for future sessions.
He told the same programme he did not think there was "anything new" in the leaders' attitudes and the economy was likely to remain the dominant issue between now and the general election in May 2015.