Yuval Levin explains how good news can emerge from the messy fight over the U.S. House speaker’s job.

Kevin McCarthy’s grueling struggle to become speaker of the House of Representatives was mostly an embarrassment for him and his new Republican majority. Yet among the fumbling and chaos, you could catch glimpses of how the House could improve itself — that is, if party factions advance structural reforms.

Such promise is not easily seen in a lot of what happened last week. Some of the Freedom Caucus members who were holdouts on Mr. McCarthy seemed to see themselves less as legislators bargaining toward policy outcomes and more as commentators hurling outrage at the very institution they worked so hard to join.

Others, however, entered the fight with valid complaints about the overcentralization of power in the House. As Mr. McCarthy worked to win their votes, it became clear that genuine structural change can be achieved by applying leverage at the right moments.

Mr. McCarthy offered a number of hollow concessions. For example, lowering the threshold for a new vote for speaker matters little, since members wouldn’t seek such a vote if they didn’t think a significant number of their colleagues would support it.

But he also committed to advancing discrete spending bills rather than another massive omnibus, like the one in December, restoring something of the order of the budget process. And he proved willing to cut into the core of the speaker’s authority by surrendering control over some seats on the crucial House Committee on Rules.

That committee determines how bills will be taken up on the floor, how much time they will get and whether and what sorts of amendments will be allowed. It is more skewed toward the majority party than the other House committees and has been under the thumbs of House speakers for decades. Surrendering seats on that committee to a faction of the party is an extraordinary and highly consequential concession.