That's probably not the right term, but we're all familiar with the concept of counter-steering and in fact I would like to propose that you can't really ride without practicing it on a regular basis. Counter-steering is something that happens as a part of the dynamics of a turn.
Conventional wisdom has it that you should force more counter-steering to more aggressively control your turn, but I'd like to propose that in some circumstances it's advisable to take the opposite action - what I'm calling counter-counter-steering.
To initiate a turn, banking your bike is accomplished by applying pressing on the handgrip in the direction you want to go, i.e. press right go right. However, what if you want to keep your bike more upright instead of leaning into the turn? The answer; you counter-counter-steer. Sounds a little screwy, but let me give you an example.
There's a shopping center off the main road I take on my ride home each day that's down a short hill. When leaving the shopping center, I pull up the hill, initiate a right hand turn, then enter the level surface of the main road. In effect, the roadbed falls away and I'm suddenly in a reverse banked roadbed situation at low speed with far more lean than I need for the turn. In addition, the main road is slightly banked for a left turn anyway, and there's frequently loose gravel or sand on the edge of the main road, so doing a low side slide out is a very real possibility. I need to reduce my lean angle to bring the bike more upright, but at over a half a ton of weight on the tires, horsing it around isn't an option.
What is needed in this type situation is to maintain turn radius, but at the same time decrease the lean angle. To do this, apply pressure to the handgrip opposite the direction you wish to turn - counter-counter-steering. The effect is that motorcycle begins to right itself. By controlling the amount of pressure you can lift the lean while still maintaining your approximate turn radius. It should be noted, however, that over-enthusiastic pressure can easily cause your bike go beyond the optimum balance point and send you over the side. This is not a tool for high speed turns! Practice and bit before you try it on the road.