You are correct about the heavy plastic covering.

Here's what I do:

The end of the sheathing has a metal cap. I'll call it a ferrule. Cut this off at the base of the ferrule. Take it off the cable, and dig out the plastic sheathing. Put it back on the cable and slide it back to the sheathing.

Now the fun part: Grab the ferrule lightly with some locking pliers. Heat the ferrule with a lighter or torch, then slide it on to the plastic sheathing. When it bottoms out, give it a 1/4 turn. This will lock it on to the plastic sheathing (via the barbs).

All this has the effect of lengthening the cable (by shortening the outer sheath)

Assembly is the reverse of removal.