Bush 41 hates Rumsfeld.
By all accounts, Cheney changed and went over to the dark side. Now, he also is on the outside looking in and will have very little influence in the White House. In fact, on the McLaughlin Group, they were even talking about the possibility that he could be gone (although they concluded that he would never resign).
Powell and Rice were neutered by the neocons. Powell was the only voice of reason and where did that get him. The neocons engineered his dismissal.
The neocons also tried to engineer Condi's dismissal. In fact, Rumsfeld would not even return her calls. Now, with the return of the pragmatists to the White House, Rice should have much more influence and be much more effective.