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U.S. Rep. Barney Frank said his committee will finalize a bill that repeals a controversial provision blamed in part for allowing American International Group to pay out $165 million in bonuses earlier this month.

The provision, added to the economic stimulus package last month, exempted bonuses previously agreed to by bailed-out companies from certain pay restrictions. This provision covered AIG, the bailed-out insurance giant which drew public outrage for its decision to go ahead with bonus payments to members of a division blamed for bringing the company to the brink of collapse.

Sen. Christopher Dodd, D-Conn., got caught in some controversy over the provision, since he initially denied involvement -- but later said Treasury officials pressured him to make the change to protect the government from potential lawsuits.

It's unclear whether repealing the provision would by itself prohibit such bonuses.

Frank, D-Mass., said the House Financial Services Committee will add the finishing touches to the new bill Wednesday. The bill would also put further restrictions on executive compensation, tying bonuses to performance.

The bill comes after the House passed a separate measure to tax such bonuses at a rate of 90 percent. But the Senate is apparently putting such legislation on hold, after President Obama and his staff expressed reservations about the constitutionality of the bill.

Senate Finance Committee Chairman Max Baucus, D-Mont., the author of another bill to tax the bonuses, said Tuesday that bill is "on pause," and that many approaches, including Frank's, are on the table.

Frank's Financial Services Committee is the third of three committees that have worked on bonus-related bills.

The House Judiciary Committee has already prepared a bill that would allow the government to sue these bailout-funded firms to reclaim the bonuses.

FOX News' Chad Pergram and Trish Turner contributed to this report.