Neither the Republican-crafted House nor a bipartisan Senate’s bill to reauthorize the Elementary and Secondary Education Act does enough to look out for traditionally low-performing groups of students, according to an analysis by the Center for American Progress, a left-leaning think tank closely aligned with the Obama administration.

To be sure, the Senate measure does contain some language calling for states to monitor district school turnaround efforts.

But just looking at the lowest performing schools, while important, doesn’t necessarily cut the mustard when it comes to making sure subgroup students (think English Language Learners or students in special education) are closing the achievement gap, CAP found.

That’s partly because some of the biggest achievement gaps are found in schools that are performing well otherwise.

The report echoes concerns from President Barack Obama and U.S. Secretary of Education Arne Duncan, who say the bills don’t go far enough when it comes to accountability. (Most folks expect some beefed-up language on the issue in a compromise bill that aides from the White House and both chambers of Congress are hard at work on right now.)

So what are the specifics?

CAP’s analysis of U.S. Department of Education data found that achievement gaps between minority students and their white peers are often bigger in high-performing schools than in low-performers. In fact, in the top 25 percent of schools, the gap between black and white students was around 15 percentage points in math, as opposed to 10 percent in the bottom quartile of schools.

And, CAP found that in 42 states, the gap between Hispanic and white students was bigger in top-performing schools than in struggling ones. And in 39 states, the gap between Black and White students was also greater in otherwise successful schools than in schools that are foundering.

And this isn’t a trivial number of kids affected. About 1.2 million black students, 1 million Hispanic students, 2.8 million kids with disabilities, 1.5 million English Language Learners, and 2.8 million low-income students go to schools where their performance trails the schoolwide averages by 10 percentage points or more.

What’s more, states with smaller black and Hispanic populations often have high proportions of schools with big achievement gaps between the performance of those kids and the school overall. Here’s a look at the states with the biggest disparities between low and high-performing schools.

CAP is recommending that the renewed law ensures that states intervene in schools with big achievement gaps, as well as in low-performing schools. And it recommends that under a renewed ESEA, schools can’t get the highest rating on state accountability systems if one subgroup is falling far behind.

Some tea-leaf reading: Again, CAP is pretty close to the Obama administration. So if they are putting out a report on subgroup accountability, that means there’s a pretty good chance it’s an issue in the mix as lawmakers try to work out a compromise on ESEA that the president can actually sign.

The trick here for negotiators—who are said to be putting in long hours with an eye to getting the bill signed by the end of the year—will be finding a way to make sure that states look out for subgroup kids while still slimming down the federal role enough that the bill can pass the very conservative U.S. House of Representatives. (Not an easy task. Good luck with that, negotiators.)