That intra-conference divide could intensify as the House Freedom Caucus (HFC) that precipitated Boehner’s exit tries to make the most of the leverage it has in the new round of leadership elections. The insurgent group is working on a list of demands to give Majority Leader Kevin McCarthy in exchange for the final votes he needs to succeed Boehner. The list is in flux, in part because the HFC’s members feel the need to achieve something that would satisfy their constituents.

The lawmakers are interested in a rule change that would ban acts of retribution against conservatives who challenge leadership — perhaps by preventing the speaker from trying to strip conservatives of their committee posts. But that effort could stall, in part because even some members of HFC understand that leadership needs a means of keeping order. “You’ve got to maintain some latitude to make it all work,” one HFC member concedes.

Another more provocative, if unlikely, option has been floated by multiple lawmakers: asking McCarthy to work to replace current committee chairmen such as Michigan representative Fred Upton, who leads the Energy and Commerce panel, with more conservative lawmakers. “They’re not too crazy about Fred Upton,” one Republican representative familiar with the HFC’s potential demands says.