Updated:9:47 p.m.

Speaker John Boehner (R-Ohio) received some much-needed good news Wednesday from the Congressional Budget Office, which credited his slightly revised deficit reduction package with cuts that exceed its debt limit increase.

The CBO’s decision to use the most up-to-date baseline when scoring the original bill showed just $850 billion in savings over the next decade, and the lower-than-expected figure sent House Republicans scrambling to rewrite it. The revised version uses the same caps on spending authority while tweaking the caps on outlays — how much agencies actually spend, not just their authority to spend — causing the CBO to credit the revised plan with more savings within the 10-year window.

But important to Boehner, the bill now meets his original target of exceeding the size of the $900 billion debt limit increase by cutting the deficit by $917 billion, something Senate Majority Leader Harry Reid’s bill does not yet do.

The Nevada Democrat’s package was scored at $2.2 trillion, $500 billion less than advertised. Reid said Wednesday that he intends to tweak his bill as well to find an additional $200 billion in cuts to match a $2.4 trillion increase in the debt ceiling.

But Reid’s cuts include about $1.3 trillion in war savings, which the GOP called a gimmick. Boehner’s proposal includes the same war spending levels, but House Republicans say they shouldn’t be counted toward deficit reduction.

After the new score, the discretionary cuts in Boehner’s bill match up almost exactly with Reid’s package, a good sign for reaching a compromise agreement.