In most of the cases during F2L, there is a moment you need to extract edge and/or corner piece(s) from a slot for pairing.
I always want to move piece(s) to the U-face and pair them at the same time in case of extract edge or corner piece extraction, to skip the pairing process.
I found many different ways in each situation to meet with it, so I chose most suitable ones for me and using them.
I will show you by my separate columns what I have chosen, dividing them by the following 3 categories.
1. Edge piece extraction (corner piece is in top layer)
2. Corner piece extraction (edge piece is in top layer)
3. Edge & Corner pieces extraction
It is necessary to compare the face color of edge piece with that of corner piece, to decide which algorithm should be adopted. So, which face should be used?
For edge piece, I decided to use F-face and B-face when it is in front and back slots respectively, and U-face when it is in the top layer.
For corner piece, I decided to use side face (R or L-face) when it is in any slot if its color is not Cross color. If it is so, then use F-face and B-dace. And U-face when it is in the top layer.