OLYMPIA — Washington state lawmakers began exploring a proposal Tuesday designed to accelerate ballot counting and allow everyone to know the winners of elections a little earlier.

A state Senate committee heard testimony on a bill that would reject ballots that don’t arrive to the auditor’s office by 8 p.m. on the night of the election. Republican Sen. Pam Roach, the bill sponsor, said she wants to find ways to speed up the process so that the results of the election come sooner, and Democrats agreed there was frustration about how long the process takes.

“What can we do to make this faster?” said Sen. Steve Conway, D-Tacoma. “I think everyone feels that we are too slow.”

As an all-mail voting state, Washington currently counts ballots so long as they are postmarked by Election Day, and that means many ballots arrive in the days after the election. Election administrators say they also have to follow strict protocols, including ones put in place after the exhausting 2004 gubernatorial count. The rules include visual scans of every ballot — front and back — to make sure marks made by voters can be ready by a machine.

Sherril Huff, director of elections in King County, estimated that it takes about a day and a half for a ballot to go through the system once it arrives at offices. She noted that the office hires extra people and has employees work extended hours and on weekends to get ballots counted.

The secretary of state’s office said it has concerns about the strict deadline proposed in the bill, but the office wants to work with county auditors to develop new ways to make the process more efficient.

“This is going to be one of my top priorities,” said Lori Augino, the state’s elections director.