COLUMBUS -- Senate Republicans directed a little more money toward Ohio's opioid crisis, and their first round of state budget changes left many school districts with less money than the House-passed budget.

Anticipating a larger revenue shortfall when new estimates are released in two weeks, Senate leaders say the revised two-year budget that takes effect July 1 is crafted to close a projected $1 billion revenue gap -- $200 million more than the hole Gov. John Kasich's budget office suggested in April that lawmakers should close.

"Let me be clear, this budget is not pain free," said Senate President Larry Obhof, R-Medina.

"We expect the current gap to increase, and the Senate has budgeted accordingly. I believe this bill reflects the right balance between funding our state's priorities and doing more with less."

The House-passed budget called for spending $170.6 million more on the drug epidemic, including $130 million for addiction treatment as well as additional support for child protection and other services. Senate Republicans said they increased that to $176.4 million, though that includes reworking some House proposals and funding them with federal dollars to make the budget math work.

The Senate is proposing $60 million for child protective services and programs to support children in drug-affected families, maintaining $20 million for the expansion of treatment housing, $6 million in new detox facilities, $5 million to help counties establish drug abuse response teams, $5 million to train teachers to identify addicted students, and $2 million for criminal and forensic labs, plus help for overwhelmed county coroners.

The Senate budget also would give two-year funding increases for 237 school districts, and cuts for 162 districts. Compared to the House-passed plan, the Senate budget means more money for 312 school districts, and less for 145.

The Senate also is proposing to eliminate the requirement for state fourth- and sixth-grade social studies tests, and eliminated a House-added provision allowing districts to use paper to take state achievement tests.

In higher education, the Senate eliminated a House-passed proposal that would have allowed universities to impose unlimited tuition increases so long as they guaranteed that tuition rate for four years. Instead, the Senate would allow for a $10 credit hour increase in the first year, and a 2 percent tuition increase for the 2018-19.

The Senate also proposed increased funding by $11.3 million for the Ohio College Opportunity Grant, a needs-based financial aid program. It would still would leave Ohio far short of the $200 million per year provided before a recession-based slashing in 2009. Still, higher-education officials are thrilled with the increase.

"It's great news," said Franklin University President David R. Decker. "It is very much appreciated when the legislature shows confidence in the importance of higher education."

Overall, many state agencies would see cuts of 3 to 4 percent. The Senate also wants to cut $200 million from Medicaid, including a $75 million spending cut to hospitals, though the overall spending cap would be lifted. "We think it's well within the range they're comfortable with," Obhof said.

Not so, said Scott Borgemenke of the Ohio Hospital Association. "Hospitals continue to shoulder a disproportionate share of burden in filling the budget gap."

The Senate also narrowed a Kasich administration proposal to divert non-violent, fifth-degree felons to community corrections settings in the 10 most populous counties.

The administration wanted to apply the program to all 88 counties, diverting an estimated 4,100 inmates from more expensive state prisons. The Senate plan would impact an estimated 1,800 fifth-degree felons.

Gary Mohr, director of the Ohio Department of Rehabilitation and Correction, called the original plan an "important step to incarcerate and rehabilitate Ohioans convicted of low level offenses in settings that will provide for better outcomes."

Senate leaders said they also eliminated tens of millions in earmarks and took about $85 million from programs with unspent funds. Democrats said they were disappointed the proposal did not address the loss of county and transit authority funding from the elimination of the sales tax on Medicaid managed care services. Obhof said it could still be worked out.

Among the other Senate budget changes:

■ Doubles to $4,000 the tax deduction families could take for the state's college savings program, or the state's ABLE program, for children with disabilities.

■ Removes many House-added provisions, such as restricting local authority to regulate lead, and putting video poker machines in racinos.

■ Increases library funding by $9.1 million.

■ Allows businesses starting in 2018 to file a centralized income tax return with the state, or continue to file with individual cities as they do currently. Cities oppose a move toward centralized tax collection.

■ Eliminates certain promotional funding for the state treasurer's office, after the House budget required agencies to get permission from the Controlling Board for any ad campaign costing more than $50,000.

The measures come after Treasurer Josh Mandel spent $2 million in state funds on a series of ads featuring him and Ohio State football coach Urban Meyer, breaking up payments into less than $50,000 each, thereby avoiding the need for Controlling Board permission.

■ Eliminates a requirement that stickers be placed on retail fuel pumps showing gas tax rates.

The Senate will make additional budget changes next week and take a full vote. From there, the House and Senate will attempt to work out differences by June 30, the end of the fiscal year.