There’s a bipartisan plan to fix part of Obamacare. Really.

A bipartisan group of legislators is working together on Obamacare — not trying to repeal it, but trying to make the law work a little bit better.

On Thursday, four Senators — two Republicans and two Democrats — introduced legislation that would tweak an Obamacare program that is meant to improve patients’ medical care, but, according to recent research, might actually be making things worse for low-income patients.

It’s hard to know now whether this change will get any traction or, like the majority of bills right now, get trapped in the political process. Still, its a notable moment for the health care law, with Senators from both political parties making an apparently good faith effort to fix something in the law that doesn’t seem to be working quite right.

The reform law tries to reduce avoidable hospitalizations, situations where patients turn up at the hospital a second time because something went wrong in their first trip. Under Obamacare, the government now penalizes hospitals when patients are readmitted within a month of discharge.

In theory, reducing readmissions is a great thing — avoidable hospitalizations are bad for patients and bad for health spending. But the story is a little different for safety-net hospitals, which are often located in urban centers and serve poor and vulnerable populations.

“We know that 16 to 20 percent of Medicare patients are likely to end up back in the hospital after 30 days,” said Ashish Jha, a professor of health policy at Harvard who has done extensive research on the topic. “Why do some people come back and others don’t? One of the other things we’ve known for some time is that poorer patients - people who live in communities with poorer health infrastructures and less social support — those people are more likely to end up back in the hospital.”

Medicare does have some ways of adjusting penalties to take into account the sickness (or health) of a hospitals’ patients. But there are still things happening outside the hospital — a lack of primary care providers, for example, or difficulty following discharge instructions — that can send lower-income patients back for a second visit.

As a result, safety net hospitals are about twice as likely to get slammed with big readmissions fines compared to other providers. Medicare is asking safety-net hospitals to work much harder — then penalizes them when don’t perform as well as everyone else.

On Thursday, Senators Joe Manchin (D-W.Va.), Roger Wicker (R-MS), Mark Kirk (R-IL) and Bill Nelson (D-FL) introduced the Hospital Readmission Accuracy and Accountability Act, which would require Medicare to account for socioeconomic status of patients when calculating penalties.

Perhaps the most surprising thing here is the fact that a bipartisan crew of politicians came together to act: on Obamacare. “The readmissions policy has been flawed from the beginning,” said Senator Kirk in a press release.

The new legislation itself won’t make Obamacare any more expensive. It’s been endorsed by the American Medical Association, the American Hospital Association, and a bevy of other provider groups.

Medicare might need to refine the way they handle this over time, but Jha cautions against letting the perfect be the enemy of the good. “The models we have for socioeconomic status adjustment are better than having no model at all,” he said. “We should do this — and continue working on new and better ways of doing it.”