Having agreed to meet in a rare evening session to vote on the three measures, representatives started bickering Tuesday over the order in which they would consider them. Each faction feared that if the bill it wanted wasn't approved first, other legislators might walk out before a vote and there would be no quorum.
Speaker Mahmoud Mashadani, a Sunni, resolved the matter Wednesday by announcing that legislators would approve each clause and then vote on the three bills as a package.
Some lawmakers complained that the strategy violated official procedure and walked out. But Mashadani and his deputy insisted that no rules had been broken, and enough legislators remained to approve the measures by a show of hands.
Mashadani, who Tuesday night had said he should disband the legislature and force early elections, told reporters after Wednesday's session: "Today is [like] a wedding celebration for the Iraqi parliament."
Before Wednesday, Iraqi lawmakers had approved only one of the bills pressed for by the United States: a measure that allows some former members of Hussein's Baath political party to return to government employment or receive a pension.
Among the three bills was another measure that figures among U.S. benchmarks for progress: a framework for relations between the central government and provincial authorities.
Wrangling over the bill had repeatedly delayed provincial elections, which U.S. officials hope will bring more Sunni Arabs into office. Most Sunnis boycotted the local balloting in 2005 and are underrepresented in the central and northern areas where they dominate numerically.
Provincial elections could also help settle disputes among the main Shiite factions, which are locked in an increasingly violent conflict for power and influence in the overwhelmingly Shiite south.
The provincial powers act includes a clause calling for new elections by Oct. 1 in all provinces except those in the semiautonomous Kurdish region in the north.
Parliament's main Sunni bloc said the bill, which provides amnesty for some of the tens of thousands of mostly Sunni prisoners in Iraqi custody, could hasten its return to government.
"We consider it an important accomplishment that the front could market to its supporters," said Salim Abdullah Jabouri, a legislator and spokesman for the bloc, the Iraqi Accordance Front.