If you're on a 2:1 friction hitch system or even a 2:1 mechanical based system system it does not lend itself to redirects, or lacing over limbs. It's one of those annoying features of having a giant loop out above you. As you ascend (closing the loop) or descend (open the loop), above you are two parallel lines, one is in motion opposite the other. There is friction at the tie-in point, minimized with the installation of some form of friction saver.
Redirects, however. simply takes a section of that loop above you into a caribiner and you choker a sling to where you want your new anchor point, biner the rope into it and you have a new tie-in point right near where you're working. However, the up-rope and the down-rope that work in opposition to each other multiply their frictional forces upon one another and create a drag that's sufficient enough to prevent the positioning advantage you're seeking.
Fabulous method for work positioning and safety. Not really an option in 2:1 climbing. Redirects are a 1:1 twin line or 1:1 SRT thing.