Democratic leaders are floating a more gradual path to a federal minimum wage of $15 per hour, which would mark a concession to some centrists who had been hesitantto back the bill for fear of aggravating small businesses, according to multiple sources familiar with the ongoing discussions.

Under the proposal, employers would have six years to phase in the wage hike rather than five.

The House plans to vote on the bill next week. And while top Democrats like Majority Leader Steny Hoyer have said they’re confident it will have enough votes to pass, they have worked behind the scenes to shore up more support and avert any drama on the floor.

Democrats also say that moderating the proposal further could ramp up pressure on Senate Republicans and the White House to drop their opposition to a minimum wage increase.

“I think there’s a recognition in every camp that the more gradual and reasonable we can make this, the more pressure there is on the Senate,” one senior aide said.

The proposed change to the bill, which has not been finalized, is also part of a strategy to avoid a last-minute failure on the floor at the hands of House Republicans.

Democrats have long worried that a GOP procedural maneuver on the floor — in which Republicans use a “motion to recommit” to put forward their own changes — could ultimately tank the entire effort.

If Republicans win support from about two dozen Democrats, they could force changes to the bill all within a few minutes. That could result in others in the caucus, including progressives, choosing to revolt and vote it down.

Heather Caygle contributed to this report.