President Joe Biden has agreed to a compromise with moderate Democrats to narrow the income eligibility for the next round of $1,400 stimulus checks that are included in a bill the Senate is expected to take up this week, a Democratic said.

That means 7 million fewer families will receive a partial payment than would have under the House version of the bill, according to an estimate from the Penn Wharton Budget Model. The new proposal will completely cut off those who earn more than $160,000 a year and individuals who earn more than $80,000 a year.

The House legislation, which passed Saturday, set the income caps at $200,000 for couples and $100,000 for individuals.

But the same households will receive the full payment of $1,400 per person, including children. Individuals earning less than $75,000 and couples earning less than $150,000 will just as in the House bill. Then, the payments will phase out faster for those earning more.

Unlike the previous two rounds, adult dependents including college students are expected to be eligible for the payments.

The House bill had already narrowed the eligibility compared to earlier rounds of stimulus payments. It still would have sent money to more than 93% of tax filers, according to estimates from both the Penn Wharton Budget Model and the nonpartisan Tax Foundation. The Senate version will deliver money to about 90% of families.

The federal government sent payments worth up to $1,200 per person last year and up to $600 in January. The next round is intended to top off the $600 checks so that individuals receive a total of $2,000.

Senate Democratic leaders are set to move the bill forward this week but are continuing to finalize the text. With a 50-50 party split, they will need the support of the entire caucus.