For CLL cases with at least one oriented corner it's possible to move one of those oriented corners to its correct position and transform to another case. This reveals why two seemingly completely different cases have a similar sequence of moves. Because there must be a correctly oriented corner, G and H cases can't be a starting point and can't be led to unless more moves are allowed. A2 and most of the D, E, and F cases have more than one set of possibilities and I've distinguished them by noting the location of certain colors on the unsolved corner within the layer to be adjusted. The moves in parentheses are optional and are only here to end the corners in the same position for each of the six orientations. My list follows Robert Yau's CLL document.
Thanks to Robert Yau for his CLL and Kirjava for the name.