Chairman Tommy Reynolds said he expects a vote in the full House on Friday. Senate Chairman Terry Burton said he expects action on a redistricting plan by Monday.
The Senate plans to release its new map Monday.
The plan for the 122 House districts reflects populations changes revealed by the 2010 Census.
The House plan reduces the number of split precincts from 449 to fewer than 200. It goes from 39 majority-black districts to 44.
It adds two new House districts in fast-growing DeSoto County. The Gulf Coast maintains its representation. The city of Madison gets its own House district, as it requested.
Read more in Friday's NEMS Daily Journal. The Associated Press contributed to this story.