Wish you were here as it is so much easier to show and my picture taking leaves a lot to be desired.  But, here is my method.  Now don't fall asleep while I type this.

Taking the wire I am going to be using I cut off enough(about 6 inches) to make an end.  I have a peice of 1/8 wire I loop this peice of wire and the flying wire around.  I use copper wire that has no coating on it to wrap with.  I also drag it thru a folded peice of sand paper before starting.  Leave enough copper wire running along the two(now 4 wires) to start your wrap up next to where the loop will be.  Right now the loop may be a little large.  Start your wrap with the copper wire keeping it tight as you can.  I make about ten wraps then set the size of my loop.  You don't want it too big or too small even tho bigger can be adjusted when done.

After setting the loop size I then lift the solid wire(separate) to make sure one of the loop wires is along side the flying wire.  Lift only enough to get the copper wire under it and put in ten wraps as tight as you can get them.  Now bring all the wires together again and do ten more wraps as tight as you can get them. 

Stay with me on this as you will repeat the next wraps as earlier with the wires lifted up a little.  After doing this for about three times do your final wraps with the wires together for about 15 wraps.  Now the copper wire you had laying along side of the flying line that was also being wrap is now twisted to the copper wire you did the wraps with.  Cut off the scrap and use a good solder and iron.  The solder shoud flow into the wraps as well as the solid wire. 

Now a warning, be careful with the handling of the lines as you will have a hard point right at the end of the wrapping.  If flexed too much it will break.  In the years of racing I have done using button hook ups I have never had a line break at the wraps.  Now at the handle end just wrap your lines like shown in the AMA rule book. 

Hope I haven't confused you too much.  DOC Holliday