The line-item veto conflict that has embroiled DFL Gov. Mark Dayton and the Republican-controlled Legislature since May 30 remains confounding and unresolved. But Minnesotans can count as good news the fact that both parties readily agreed Tuesday to tap former Judge Richard Solum — an accomplished mediator — to mediate their dispute.

Solum has an impressive track record of finding middle ground in high-profile disputes. Appointed to the Hennepin County District Court bench by former Republican Gov. Arne Carlson, Solum stayed just six years on the court, then became a mediator in cases of public importance that included a land value dispute at what became Target Field in 2007, former University of Minnesota basketball coach Clem Haskins’ buyout terms in 2002 and a liability dispute in 2014 involving the Ponzi scheme that landed Tom Petters in federal prison.

We hope that background prepares Solum for the stubborn resistance to compromise that he’s likely to find in his latest assignment. And we hope the Minnesota Supreme Court, which ordered mediation and set a Sept. 30 deadline for a report on its progress, is prepared to act if Solum’s best efforts prove futile and the Legislature’s operating funds run out. Minnesota should not be deprived of a functioning legislative branch of government.

But our highest hope in this matter is for legislators and Dayton to surprise Minnesotans by doing what they have so often failed to do in the last several years. With or without the help of a mediator, they should relieve this state of the uncertainty and dysfunction that the line-item veto dispute has brought. They should make a deal.

Dayton’s May 30 letter announcing the line-item veto of House and Senate operating budgets spelled out five matters of dispute in the just-concluded legislative session that he wants repealed, despite having just signed into law large omnibus bills containing those provisions. (Packing multiple subjects into a few large bills is a constitutionally questionable bad habit that the Supreme Court should help the Legislature break.)

Three of the provisions at issue involve tax cuts for business property owners, inheritors of large estates and tobacco purchasers. These cuts are designed to take an ever-increasing bite from state revenues in future years. Dayton is right to be concerned that those measures put the state at risk of future deficits. But they appear to be affordable in the current state budget. One possible compromise: make those tax provisions expire at the end of the current biennium, giving the new governor and Legislature in 2019 another chance to judge their affordability.

The other two matters of dispute seem similarly susceptible to deals that allow for future legislators to take a second look. One involves driver’s licenses for undocumented immigrants; the other, changes in licensure standards for teachers. Adding time limits to the policy changes the Legislature seeks would turn the 2017 changes into de facto pilot projects, allowing future lawmakers to assess their worth before continuing them.

Those are a few of many possibilities for moving this extraordinary dispute toward the more ordinary give-and-take that Minnesotans expect when control of state government is divided between the two major parties. Both parties may see an advantage in refusing to bend to Solum’s efforts at mediation. If they do, they’re looking for partisan advantage and short-term gain. We suspect that Minnesotans would much prefer that they look out for this state’s long-term interest in maintaining an operational and orderly state government.