Even as a bipartisan majority in the state House celebrates its renovation to the budget proposal of Gov. Bobby Jindal, the spotlight moves to the Senate, where a new phase of budget deliberations begins.

If history is any guide, the Senate will consult with the governor on changes to the House-passed product. But the significance of the gesture toward independence in the House is that history might not be as good a guide as it used to be.

At issue will be the House’s efforts to take what members considered one-time money out of the operating budget. Definitional matters aside, and there’s dispute about what one-time money really is, the House budget will draw fire because it is reliant on its own budgeting gimmicks, including a multi-year tax amnesty for big companies.

If senators might look askance at some of the House handiwork, the governor remains an obstacle to the idea of raising some revenue through suspension or reduction of some corporate tax breaks.

Amid these cross-purposes and conflicting goals, the Senate sits in a position either to claim the mantle of legislative independence, or not — but the latter option does not preclude a deal in which the governor gives ground on some revenue increases on the tax breaks.

If history is any guide, Senate leaders will look for what can pass muster with the governor as well as what can command a majority in the House when the budget returns to the lower chamber.

The House must concur with Senate changes to complete the deal and avoid an anything-goes conference committee. Senators are in a stronger position relative to the governor because the House’s votes put Jindal on a bit of the defensive.

Much strategizing is going on in the Senate offices. If history is any guide.