Capture the cutting stones in joseki 1
It is really Black's decision and not White's, because White must capture the cutting stone in order not to get an inferior result.
Jonahx: This is a place where reading out the ladder is helpful (as it usually is) Becuase the ladder would have to cross a large part of the board, there very well may be a ladder breaking stone somewhere, especially if this is later in the game, in which case may not be such a bad move.
togo: The problem is that White now has to invest another stone to get life. Compare to the situation when is on the other side - then even smaller life would be sufficient.
Black can get the outside influence by cutting at the other side, forcing White to capture the cutting stone. The big difference with the previous diagram is that White lives already by the ponnuki. You could say White has sente. This is a fair exchange.
togo: Again the real problem is that white now has to invest another stone. If the whole exchange (including an extension) would be gote for black, all would be fine.
There is more discussion on the second page.