— South Carolina’s unemployment agency reports that it’s overpaying less and recouping more of the excess benefits it does dole out. But state senators said Monday the numbers are not good enough.

“We’re certainly heading in the right direction, but we’ve got work to do,” said Sen. Thomas Alexander, whose Labor Commerce and Industry Committee will grill the next leader of the Department of Employment and Workforce on the subject.

Gov. Nikki Haley named Cheryl Stanton as her choice for the Cabinet agency last week. A labor lawyer in a New York City firm, Stanton formerly worked for the U.S. Department of Labor under President George W. Bush.

Alexander has not yet set a confirmation hearing schedule.

Most overpayments are due to people claiming they’re still unemployed after getting a job. Whether they’re lying or don’t understand the system, overpayments result, said interim director John Finan.

In those cases, DEW employees initially made correct decisions based on the information they had, he said, but crosschecks later with employment rolls discovered the persons actually were drawing a paycheck and had been improperly paid for weeks or months. That includes part-time jobs that should reduce weekly benefits.

Another part of the problem is businesses either failing to report or not reporting in a timely manner their new hires to a database as required, delaying errors being caught, said Finan, who became interim director for a second time after former director Abraham Turner resigned Feb. 15.

According to the agency, those two issues accounted for a combined 80 percent of overpayments in the last half of 2012. Mistakes attributed fully to the agency comprise 5 percent of those recent overpayments, down from 40 percent of all overpayments in 2009-10, when the Legislature overhauled the agency and put it in the governor’s Cabinet.

Legislators have remained highly critical of an overpayment rate that spiked to nearly 18 percent of all benefits paid in 2010-11, representing about $69 million. The rate dropped to 11.6 percent for the last six months of 2012, according to the most recent numbers from the federal labor agency. Of that estimated $15.5 million doled out in excess, the agency got back about $8 million, Finan said.

“I think you’re going to see that rate continue to go down. The overpayment amount is not going to be such an eye-popping number anymore,” he said.

While that’s progress, “it’s not zero,” said Sen. Kevin Bryant, R-Anderson, a vocal critic of the agency. “Employers are having to pay this.”

Finan expects the rate to be 10 percent by summer, and for the agency to collect the bulk of it back, thanks partly to a program launched in January that allows for reimbursements through federal income tax returns.

“Before, it was pretty hard to get money back from an unemployed person, but they eventually file for federal income taxes, and they get credits. We now can go after that and are doing so,” Finan said.

For the first three months of the year, the agency collected $16 million in reimbursements through all methods, including the offsetting of future benefits and the seizing of state income tax refunds.

To catch more errors, and faster, the agency is working with the Department of Social Services, which is responsible for employers’ new hires database, to compile the data every 15 days rather than once a month, Finan said. That could require legislative action.

A bill approved by the House and awaiting action in the Senate would add penalties to businesses that don’t report new hires. It would also allow the agency to charge those who fraudulently receive unemployment benefits a 25 percent penalty, in addition to requiring a full reimbursement.

According to the federal labor department, an estimated 4 percent of South Carolina’s overpayments were due to outright fraud in fiscal year 2011-12, down from 7 percent the previous year.

Last year, the agency launched an effort to clamp down on such fraud, going after people who owe more than $10,000. Since Jan. 1, eight people who owe a combined $115,000 have been arrested.

DEW also recently began cross-checking the Department of Corrections’ inmate lists. So far, $58,000 worth of potential overpayments to people imprisoned — and therefore obviously unable to work as required to receive benefits — has been forwarded to the agency’s collection office, said agency spokeswoman Adrienne Fairwell.