Most of the comments are correct but beware UV with these low-stretch, high-strength materials - They rot very quickly in the sun. Jmolan has the right idea but I carry it farther and entirely replace the cover. There's all sorts of constant diameter splices. Make sure the one you're using doesn't depend on external whipping or have feathers less than sheave diameter, to prevent bulging.
Unlike a lot of professional riggers, I like StaSet-X: It's cost/strength & stretch ratios are superior to anything else and it's easy and quick to splice. The main problem people have with it is it becoming more and more stiff with time. That's because they are twisting their lines. The solution there is to use butterfly coils instead of traditional coils, which really don't make much sense in the vast majority of uses aboard or kern-mantle (cover and core) rope. They're holdovers from 3-strand hemp rope.
I'm a shipwright, rigger and professional sailor, in business as My Boat Works, in Los Angeles. I also make super quality, High-Definition instructional boating movies! I'm here to give my expertise to boaters, as I was helped. It's my pleasure to help you enjoy activities I love so. Cheers! - Jerr