The Commons authorities were urged today to scrap an arrangement that allows MPs to admit expenses errors and repay money in secret.
Dozens of individuals have been dealt with under a "fast-track" scheme for handling complaints about their claims.
The "rectification" procedure was introduced in 2005 when Michael Martin was the Commons Speaker.
MPs who are willing to admit they have broken parliamentary rules can be given the option of making amends and apologising privately to the Standards and Privileges Committee, which oversees conduct issues.
The latest annual report by parliamentary standards commissioner John Lyon reveals that 16 MPs struck a deal to use the scheme in 2008-09.
None of the cases involved personal allowances, according to a spokeswoman for Mr Lyon.
Eight were said to have related to use of stationery, and six to spending under the Communications Allowance. Two MPs filed claims too late, while one admitted errors in the use of a parliamentary email account.
The spokeswoman insisted that not all of the cases involved repayment of money, although she declined to say how many did.
In 2007-08 the rectification procedure was employed on seven occasions, and in 2006-07 it was used 10 times, she added.
The spokeswoman denied that the process was "secret", stressing that it was in the standing orders of the House. She insisted the increase in cases was proportional to an increase in workload as more attention was focused on MPs' expenses.
Figures for 2009-10 will not be published by the commissioner until June, but it is understood that Labour backbencher Janet Anderson is among those who have been fast-tracked over the period.
She is said to have apologised and repaid almost £5,750 privately after overclaiming petty cash.
Lib Dem MP Norman Baker told the Daily Telegraph that the practice should be brought to an end.
"When someone has admitted to doing something wrong, and certainly when they're paying back money, then that's a matter that should be public," he said.
"Constituents deserve to know how their MPs are acting in a public capacity.
"And where public money is involved, we have a right to openness and accountability."Reuse content