Sounds like you are describing an aircraft in proper trim. I am nobody's pilot, but I have heard that a properly trimmed aircraft will neither gain nor lose altitude in straight flight, so the pilot can take his hands off the yoke (and no autopilot, of course) and the plane will continue on in a straight, level path.
Do aircraft still use some modern version of the old Ryan Stormscope? Paul Ryan (not the Congressman) is one of our alums:
Good Buckeye Engineer