If they succeed, they will reverse a trend that began with Democrats in the 1970s but reached new heights with the Republican takeover of 1994. The incoming speaker at that time, Newt Gingrich, centralized power in the leadership suites and moved it away from committee chairmen, requiring them to win the approval of the leadership team.

The conservatives’ demands, including a long list of proposed rules changes, are made clear in a revealing questionnaire that they drew up for candidates seeking to replace Mr. Boehner.

On Friday, the conservatives said they would demand answers to the same questionnaire from Representative Paul D. Ryan of Wisconsin, whom many Republicans are imploring to run for speaker, should he decide to seek the post.

The changes would include stripping the speaker of his outsize power over the Republican steering committee, which appoints the chairmen for all committees as well as for Appropriations subcommittees. The changes would also reduce the leadership’s tight control over what bills and amendments reach the House floor.