Controversial plans to carry out MPs' expenses investigations in secret have been criticised by sleaze watchdogs.
Under proposals from the Independent Parliamentary Standards Authority (Ipsa), politicians will no longer be named when investigations are launched.
Compliance officer Peter Davis said the change would balance the "public interest in transparency" with "operational needs and fairness".
He highlighted the "reputational damage" to MPs caused by naming them before investigations are complete.
The measure, put out for consultation in September, has come under fire for making the Ipsa regime less transparent than the one it replaced in 2010 - when the identities of those under investigation were routinely confirmed.
And both the cross-party Standards Committee and the independent Committee on Standards in Public Life (CSPL) have now voiced concerns.
The CSPL said the proposal was "not consistent with the principles of openness and transparency which underlie the scheme".
Responding to the consultation, it also pointed out that the parliamentary standards commissioner routinely named MPs they were investigating.
"The CSPL is not convinced that practically the change proposed would achieve the outcome in every case Ipsa is seeking, as presumably Ipsa cannot prevent an individual complainant, or a leak, disclosing the fact of a complaint, which may, if publicly released, result in the same impacts the changes are aimed at avoiding," it added.
The Standards Committee's response warned: "There is clearly a difficult balance between transparency and the fair and efficient conduct of investigations.
"We consider it is possible that the changes proposed in the consultation may tilt the balance too far from transparency ...
"We invite Ipsa to consider whether the advantages of removing the assessment stage outweigh the transparency brought by the current system, in which names are released if it appears there may be grounds for investigation."
If the proposal is implemented it will be Ipsa's second U-turn on the issue.
Initially the watchdog's rules indicated that the names of MPs under investigation should be released when probes were launched, but the body's compliance officer Luke March then refused to do so on the basis it was "unfair".
He subsequently resigned and a consultation in 2011 concluded that the identities should indeed be made public during formal investigations rather than afterwards.
As a result, ongoing investigations are currently declared on the watchdog's website.
The Standards Committee did support plans to bar the public from hearings with MPs on alleged expenses abuses.
"In this case, we agree that private hearings strike an appropriate balance between fairness and transparency, although we recommend the transcript of any such hearing should be published by the Compliance Officer at the conclusion of any investigation," it said.
The CSPL also did not oppose the change, as long as written transcripts were released.