adding cover

[Brion Toss]

Hello,
You have some options here. The simplest is to start with a piece of double-braid Dacron, the core of which is about 3/8". You can err on the small side in all likelhood; the new cover can bunch up a bit to swallow more. Tape the Spectra rope to the core, using lengthwise strips of blue masking tape, then reinforce with a very few spiral wraps, with very little overlap. Bunch the cover by pulling the core out the other end, then run the line through as you bring the core out. Alternatively you can milk a Wand or fid through, but it is usually slower.
Depending on the application, you might want a cover with extra abrasion- and heat-resistance. Contact a vendor or rigger for details. in any event, finish by whipping the end down to the rope.
You can also insert a core within the core, which is neater. Just put the largest rope in the core that the cover will be able to swallow. This requires marking the winch location on the rope, pulling the core out partway (either from the end or in a bight, depending how close to the end you are), inserting the extra piece, with ends nicely tapered, then pulling the core back in.
Fair leads,
Brion Toss