George Osborne should consider "phasing in" planned tax credit cuts or only imposing them on new claimants, according to a think-tank founded by Cabinet colleague Iain Duncan Smith.
The Centre for Social Justice (CSJ) insisted the Chancellor could use this month's Autumn Statement to ease the impact of the controversial changes without risking his drive for a budget surplus.
In a report, the organisation warned against taking money from Mr Duncan Smith's flagship Universal Credit scheme to sweeten the tax credit pill.
It pointed out that the UC reforms meant by 2020 only 9% of those currently getting tax credits would still be receiving them.
Instead, the think-tank suggested the Government could help people to work more hours or introduce a transitional fund for those hardest hit, as happened with the benefit cap.
Another option would be to slow and phase in tax credit cuts in line with increases in the national living wage and personal allowance. This would still allow him to achieve "structural change" and £4 billion of annual savings by 2020, the report said.
The most expensive course would be only imposing the tax credit cuts on new claimants - but the authors note that it would have the "least social and political cost".
CSJ chief executive Baroness Stroud, a former special adviser to Work and Pensions Secretary Mr Duncan Smith, said: "There are no easy choices, but these are the options the Chancellor has.
"What he should not do is raid Universal Credit to pay for any transitional changes or he will be recreating the same problem there.
"The projected savings through changes to tax credits is £4.4 billion, the Government plans to turn a surplus of £10 billion in 2019-20 and of £11.6 billion in 2020-21.
"Why have a surplus if we can't protect those on the lowest pay, doing the right thing by taking work?
"The Chancellor can protect these workers and have a surplus by 2020.
"This Government is set to achieve its historic aim to make sure work always pays more than welfare, we shouldn't put that at risk."
Meanwhile, the Commons Work and Pensions Committee has again demanded information from the Treasury about movements on and off tax credits and how long people claim for.
Chairman Frank Field said: "In devising and costing its tax credit reform and amendments to it, the Treasury must have crunched at least some of the numbers around flows of people on and off tax credits, just as they must have the analysis that we and the Treasury Committee have asked for of the true picture of the net impact of the proposed tax credit cuts.
"So the fact that they have not produced these data must mean either that they are sitting on it for reasons of their own, or that they are going into all these policy changes as blind as we are. Both scenarios are almost equally worrying."