Ministers said they wanted consensus on key reforms
The government has dropped plans for a legally-binding code of conduct for MPs after fears it would prompt a flood of legal challenges.
The idea had been a key part of the government's plans to "clean-up" politics after the expenses scandal.
But former standards watchdog Sir Philip Mawer warned it was a recipe for "delay, cost and confusion".
Ministers are to press ahead with plans to set up an external body to run the MPs' expenses system.
Only three days of debate have been scheduled for the Parliamentary Standards Bill as the government wants it passed before MPs leave for the summer recess on 21 July.
Lawyers' 'field day'
The bill would hand the day-to-day administration and oversight of MPs' expenses to an external body.
Earlier Sir Philip, the former Parliamentary Standards Commissioner, told a separate inquiry into MPs' expenses the legislation was "confused" and warned that a legally binding code of conduct could create a "rules-based system which lawyers will have a field day with and which may well cost the public more".
The Clerk of the House - the Commons' top official Malcolm Jack - has also warned of legal challenges to any code drawn up by MPs which "in the present climate" might mean "no shortage of potential litigants trying to make a point".
MPs debating the bill on Monday raised concerns that lack of sufficient scrutiny will lead to long-term damage to how the institution functions.
"There are some really serious issues about the role of Parliament in this bill and I am very worried that we are rushing it through," Sir George Young, chairman of the committee on standards and privileges, said.
Earlier he said he wanted to be "held accountable to the ballot box, not to the courts, for what I do as an MP".
Justice Secretary Jack Straw said the measures had to be agreed quickly because of Parliament's "collective" failure over expenses.
"The expenses scandal was not just a matter of a couple of headlines," he said.
"It has engulfed this House and its reputation. We face a really serious problem in terms of rebuilding public confidence."
But he agreed to drop a clause introducing a legally binding code of conduct on non-financial aspects of MPs' behaviour which could have stipulated, for instance, how many surgery hours they offer.
Instead the code will be incorporated into the clause of the bill dealing solely with MPs' financial interests.
Mr Straw said he was acting in the "interest of consensus" after several MPs and Parliamentary officials had expressed concerns about the measure's likely consequences.
The bill passed its second reading with a majority of 290.
For the Conservatives, Shadow Commons Leader Alan Duncan welcomed the climb-down, saying "we can't end the culture of blank cheques to MPs, only to open up a culture of blank cheques for lawyers".
However, Mr Straw refused to give ground over the inclusion of three new criminal offences in the bill governing MPs' financial dealings.
These would see fines and a potential 12-month jail sentence for MPs who area found to have knowingly made false claims, failed to fully declare outside financial interests or breached the rules on paid advocacy.
Several Tory MPs said the offences were unnecessary and redundant as the offences were already covered by existing laws on fraud and theft applicable to MPs.
"Having offences in this Bill are fundamental to its proper operation and, above all, fundamental to ensuring public confidence in this scheme," Mr Straw said.
Meanwhile, during a separate independent inquiry into MPs expenses, another former parliamentary standards commissioner, Elizabeth Filkin, said the crisis was avoidable.
She was removed as commissioner in 2001 after angering many MPs through criticism of their conduct.
She told the Committee on Standards in Public Life, which is looking into MPs' pay and expenses, that Parliament was a "very insular place and people feel entitled to all sorts of privileges of one kind or another because of their position".
She said it was "very sad" that "people at the top" did not do enough to ensure "the right sort of standards".