Lord Bach, Labour's shadow justice minister, said the amendment was "extremely cautious" but "humane" in the way it was described.
Peers backed a motion from former Labour justice minister Lord Bach, which "regretted" the coalition had broken a promise on exemptions.
Later, shadow justice minister Lord Bach called for the preservation of free legal support for people challenging cuts to their benefits.
Replying for Labour, shadow justice minister Lord Bach described the proposal as a "very important statement of principle" which he supported wholeheartedly.
Lord Bach said claimants appealing against a ruling on their welfare benefits would get no legal aid at the start of their case.
Lord Bach, replying for Labour, said that current divorce law leads to "too much uncertainty" for couples trying to come to financial settlements.
Opposition spokesman Lord Bach said any amendment proposed by the two peers deserved "careful" and "sympathetic" consideration because of their experience and backgrounds.
Peers backed a motion by Labour's Lord Bach accusing ministers of failing to honour a previous commitment on access to help in welfare cases.
Shadow justice minister Lord Bach argued it would discourage oral hearings, which he said tend to have a higher success rate than written hearings.
Replying for the opposition, shadow justice minister Lord Bach accused the government of keeping its policy on self-defence laws "under wraps" since the justice secretary's recent conference speech.
Farming Minister Lord Bach said the UK was well placed to develop a competitive market in energy crops, and the farming community was keen to embrace new opportunities.
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Junior justice minister Lord Bach told peers that trust among the electorate had been "profoundly damaged" and the government had to do "all that we can" to rebuild it.
Lord Bach said the government was offering financial support to farmers who chose to grow short-rotation coppice, like willow, to help them make ends meet while the crops grew.
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But Labour's Lord Bach, a junior justice minister until the change of government, pointed to the discrepancy between the former views of the two parties in the ruling coalition.
Shadow justice minister Lord Bach - the former legal aid minister - said he agreed mediation could be used in more cases but said that it "doesn't come cheap either".
Lord Bach called on the government to allow for "real compromise" on its proposals, arguing that it was essential for legal aid to remain available in areas such as medical negligence.
For the opposition, shadow justice minister Lord Bach said knife crime had been a "scourge" on communities throughout Britain, but he accused the government of playing a "game" of "legislative public relations".
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Leading the wind up speeches, Labour justice spokesman Lord Bach referred to the many peers who had raised concerns about changes to legal aid, praising the level of legal expertise that had been on display in the House.
Labour's Lord Bach has one on access to legal advice for people challenging rulings on their benefits, an issue which has led to some ill-tempered exchanges with the Lib Dem leader in the Lords and Justice Minister, Lord McNally.
The government has said it will allow legal aid for some appeals to upper tier tribunals in social welfare cases, but Lord Bach put forward an amendment that would allow funding to be provided in a much wider range of cases.
Former Labour minister Lord Bach said the government had failed to honour an earlier commitment by former Lord Chancellor Kenneth Clarke to allow support in "point of law" cases at the first-tier tribunal level - the first stage of the tribunal process.
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