How do you go up a tall wall?

Occasionally in Dustforce I'll come up against a tall wall with crud fairly high up where a double-jump + a little wall run will just barely get me into it, but I lose momentum and fall. Sometimes I'm able to get up with enough speed to keep running, but I don't know what I'm doing other than getting frustrated at the controller.

When I'm successful, it seems like I can hop off and on the wall quickly, but when I actually try to jump off and on I can't air-jump back on and I just fall.

How do you go up tall walls (not shafts where you can ping-pong back and forth)?

This is how to get the maximum height from a vertical wall:

1. Jump from the ground onto the wall (you get more height than running straight up it from the ground).
2. Run up the wall till you cannot go any higher.
3. Jump away from the wall.
4. At the apex of the previous jump, jump again towards the wall.
5. Run up the wall till you cannot go any higher.
6. Jump away from the wall.

Here's an image with those steps: