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".
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.