A £150 million package to deal with legacy issues should prioritise compensation for victims over investigations, eight high-profile peers have said.
The group, including Chris Patten, who oversaw the creation of the PSNI, and four former Secretaries of State, make the argument in an open letter to current NI Secretary Karen Bradley.
They caution against spending money on costly investigations which may never deliver justice.
A public consultation on how to deal with the past ended last Friday. It proposed a Historical Investigations Unit (HIU), separate from the PSNI, to examine around 1,700 Troubles-era deaths.
The Government has already pledged £150m to support legacy reform in Northern Ireland.
However, in their letter, the eight peers argue the focus must be to "resource victims, not investigations that have little or no likelihood of either prosecution or alternative closure satisfactory to victims".
The signatories include Lord Patten, whose reforms to policing in Northern Ireland led to the creation of the PSNI, and Conservative peer Tom King, who served as Northern Ireland Secretary from 1985 to 1989.
Three former Labour Secretaries of State - John Reid, who held the post in 2000-01, Paul Murphy (2002-05) and Peter Hain (2005-07) - also put their names to the letter.
The other signatories are former Church of Ireland Primate Robin Eames, who co-authored a report on dealing with the past in 2008, former Northern Ireland Affairs Committee chairman Patrick Cormack, and Des Browne, an ex-NIO minister.
Lord Hain, who co-ordinated the letter, said that while they were proposing a line be drawn under the past, they were against an amnesty. He said: "We are not proposing an amnesty but an even-handed approach to this which does not just target members of the security forces."
Lord Hain said they would not oppose the pursuit of a case if significant new evidence emerged.
The letter acknowledges the "great importance" which many victims' families place on the prosecution, conviction and sentencing of perpetrators. But it goes on to set out how only a small number of investigations into the past have led to prosecutions.
It states: "The Historical Enquiries Team completed work on 1,615 cases involving more than 2,000 deaths. We have been authoritatively informed that, of all those cases, only 17 were referred to the Public Prosecution Service and only three resulted in prosecutions and convictions for murder."
Noting that the HIU will have a caseload of around 1,700 deaths, the letter warns the number of prosecutions and convictions is likely to be very small. It adds: "It must be worth at least pausing to consider whether this is the best possible use of £150m."
The past has been one of the key sticking points between the DUP and Sinn Fein during talks to break the political impasse. The pursuit of former soldiers has also sparked outrage among the veterans' community.
The letter states past cases must be treated in an "absolutely even-handed manner".
It adds: "We note that currently prosecutions are being considered for former members of the armed forces - perhaps because records and information are more readily available - but none so far as we can establish for paramilitaries. That cannot be right.
"We believe that it is essential to treat past cases in an absolutely even-handed manner. That also means former military personnel cannot be exempt (as some are suggesting) while other former combatants, either loyalist or republican, are pursued."