Ok, so here's my new method for permuting 3x3 edges, I call it "M2
method". It's very simple, fast, and 100% intuitive so you don't need
to learn a single alg for it.

Of course it's a 2-cycle method, one piece getting solved each time.
The piece to be solved is at FD. Since I can't just swap two pieces, I
need to have some side effect. Here it is swapping (FU,BD)+(U,D)+(F,B)
. Note FU and BD are solved relative to the M centers.

Here's an example solve, using scramble #28 from post #754 (http:
//tinyurl.com/lytqj). It's ready to be pasted into this page:
http://thearufam.brinkster.net/cube/wrapplet.asp

-------------------- start --------------------
[Scramble] U2 D2 L' U D2 R2 L2 D R D' B2 U D' F2 R2 U' F2 R2 B2

[solve LU] (L U' L' U) M2 (U' L U L')
[solve LD] (U' L2 U) M2 (U' L2 U)
[solve RF] (U R U') M2 (U R' U')
[solve RU] (R' U R U') M2 (U R' U' R)
[solve BD] M U2 M U2
[solve LF] (U' L' U) M2 (U' L U)
[solve RD] (U R2 U') M2 (U R2 U')
[solve FU] M U2 M U2
[solve RB] (U R' U') M2 (U R U')
[solve LB] (U' L U) M2 (U' L' U)
--------------------- end ---------------------

For M2 I use Joel's finger trick, i.e. L (l' M'), using my left ring
finger to pull the M'. My left middle finger holds the B stickers of
LB+LBD, so my ring finger is free for the M' and my index finger is
free for U'.

Oh, and actually it was a bad choice to have BU already solved. It's
the easiest to solve, it looks like:
[solve BU] M2

So, how do you like it?

Cheers!
Stefan