The last election of the 2006 cycle will be the first election of 2007.
Voters will decide Jan. 16 who represents northern Brazoria County and Matagorda County -- a week after the Legislature begins its new session.
The runoff election between two Republican businessmen from Pearland will be the fourth election for Texas House District 29.
"One thing about it, everyone will know who we are," said Mike O'Day, who is in the runoff with Randy Weber. "We'll be the only one being sworn in on that day. It'll be good publicity."
The runoff will cost Brazoria County about $16,000, said county elections director Janice Evans. Early voting begins Monday and extends through Friday from 7 a.m. to 7 p.m.
One popular early-voting site, Pearland's Westside Event Center, wasn't available for this election, Evans said.
The only early-voting site in Pearland will be a Justice of the Peace courtroom at 3801 E. Pear.
Other early-voting locations in Brazoria County will be at the Alvin Library, the Courthouse North Annex in Manvel and the Courthouse Annex in Angleton.
Voters who didn't cast ballots in the special election can still vote in the runoff.