Topeka ? The House has advanced a bill that provides a one-year, $137 million increase in state aid to schools and gives local school boards more flexibility to raise property taxes.

But no mechanism for providing the additional aid is identified in the bill, tentatively approved Tuesday, 73-49. Final House action was scheduled for Wednesday, when passage would send the measure to the Senate.

The $137 million represents the first year of a larger plan by Gov. Kathleen Sebelius. Her package would increase aid to school districts by $304 million over three years through higher sales, property and individual income taxes.

The House rejected the governor’s three-year plan on a 71-44 vote before endorsing the smaller version, which would raise state aid per pupil by $100 and put more money toward helping poor and minority students’ academic performance. State aid to schools now totals about $2.6 billion a year.

Also under the bill, school districts could increase local option budgets — financed with property taxes — from the current cap of 25 percent to 30 percent of their total general fund expenditures. Ninety of the state’s 302 school districts have reached the limit.

The school finance provisions were attached to another measure that raises the state’s $6,000 standard income tax deduction for married couples to $20,000, which House members said would create a $150 million tax break.

“This is a pretty dysfunctional bill,” complained Rep. Steve Huebert, R-Valley Center.

Two weeks ago, the House ended debate on the same combination of education proposals after they appeared to have support and Sebelius telephoned members on the floor.

“There’s some impatience on school finance, and I understand that,” said House Speaker Doug Mays, R-Topeka.

Raising the local option budget is critical for school districts that have reached the 25 percent cap, but Mays said it’s not solely a Johnson County issue, as it once was.

“The core piece is the local control piece,” Mays said.

Despite the rejection of the governor’s plan, her fellow Democrats in the House said Tuesday’s debate still was a step toward satisfying the concerns raised by a Shawnee County judge’s preliminary order finding constitutional flaws in the current school finance system. The state is appealing that order.

Some of the support Tuesday “was purely political,” but the debate showed that the House can achieve compromise between increasing statewide school funding and letting local boards do more on their own, said House Minority Leader Dennis McKinney, D-Greensburg.

Mays stood by his earlier statements that no significant changes in the funding formula will be made in the current session, although efforts to increase funding would be considered.

“I think the debate really begins this week,” he said.

The Senate rejected Sebelius’ proposal two weeks ago, but Republican leaders there promised to begin work on a new school finance plan.

In other action Tuesday:

— Kansas courts could hire 27 more employees — including a judge and three magistrates — under a proposed judiciary budget endorsed by a House panel.

— Legislation suspending the state’s new destination-based sales tax system until Congress allows taxation on Internet purchases won House approval.

Sebelius’ proposed $243 million corrections budget, increasing spending on the prison system by 1.9 percent, cleared a House committee.