I didn't particularly like making a slipped overhand and then pulling the loop back part way.
This stage was meant to be an easy memorisable, not easy tied. Everybody knows and can remember how to tie a slipped overhand knot.
Do not forget that I work with climbing 10mm+ ropes, not with smaller material, where to pinch a bight of the overhand and pull it away would require some dexterity, indeed.
I believe that you and Luca still have not realized what you really do, because you do it by tyng the same things, with a different order...You make a first bight, right ? This is the first bight of the 3-bights method. See your fourth picture. There you have two bights, the one half-reeved through the other - and both of them been twisted 180 degrees around their axis. So, this is the first and the second bight of the 3-bights method, only that I form the bights separately, in different parts of the line, and only then I "wear" the one through the other half way - you make the same thing, but you form the second bight around the neck of the first in its final place, you do not form them at different places of the line, and then wear the first through the second. I believe that "my" method, which is Ashley s method, of course, is simpler conceptually, easier to memorize, and more general, since with the same METHOD. just by altering details, you can tie many knots ! At the final step, Ashley s method and your method are identical, because you reave the third bight through the opening of the half-reeved one( fifth picture ). You may not see your third bight, but its material is there, where it has been from the star : in between the first and the second bight. It is the "bridge" between the first and the second bight.
If you do the same thing, but, for the third bight you use material of the line beyond the first two, you can tie mid-line eye-knots suitable for directional pull, like what we need in Trucker s hitch. See :
http://igkt.net/sm/index.php?topic=1870.msg21210#msg21210 http://igkt.net/sm/index.php?topic=1870.msg21216#msg21216 I do not have a good memory, and I hate to be forced to memorize things that are not connected to each other with some logically coherent order. So, I prefer methods that are quite general, and where I can see some inner logic, some rationale. That is why I prefer the 3-bights method, in its "pure" form I described at the thread about the pet loops. The second, more special method I describe here, at Reply#11, was just an attempt to find something quicker, that would be as "simple" as the particular very simple knot itself.
JP, please, do what I had suggested to kd8eech :Tie all the knots the 3-bight method can generate, first with the bights as they are, without been twisted 180 degrees around their necks, and then by twisted bights, in every combination : one of them twisted clock-wise or counter-clockwise, two of them, both twisted at every possible combination of clock-wise and counter-clockwise turns, and, finally three of them, also twisted in every possible of the two twists each. If you tie all those eye-knots that you can tie this way, you will appreciate the 3-bights method, in particular, and a METHOD, that is, a general scheme of things, in general.