I recently acquired a crazy quilt top in need of some help-a couple of the silk patches are frayed. I'm a complete newbie to quilting (nothing like jumping in at the deep end, right? My other project is an axehead...), but would like to replace these pieces, back the quilt, and use it as the couch napping quilt.

I understand from basic Google research that it shouldn't be batted, and should be tied as opposed to machine quilted, and probably doesn't need to be bound, just enveloped.

After that, I'm a little lost. How do I go about replacing the pieces? One frayed spot is small enough that I can applique over it, and I've got a lot of vintage tatting pieces around that would do nicely.

The question is what do I do about the two bigger pieces? The one is so frayed it's almost completely gone; the other is still present, but barely (and is the same fabric as the mostly-missing piece, so I suspect it's headed the same way).

Any words of wisdom on how to go about doing this?

quilting is a very personal craft, you can give it all of your own unique touches or you can follow a pattern exactly. a crazy quilt is no different. if you want to tie it, that is fine, as is hand or machine quilting. The trick is doing what looks good to you! I am not sure what is meant by no binding....I think a binding helps keep the edges secure. But again, that is what I think....everyone is different.

IMHO, I would stitch something, use lace, use SOMETHING over those pieces rather than remove them. Fancy stitches, another applique, a big button, or a combination of anything might work. If removed, you may be faced with many, many cross seams (nature of a crazy quilt) and do more harm than good.

I understand from basic Google research that it shouldn't be batted, and should be tied as opposed to machine quilted, and probably doesn't need to be bound, just enveloped.
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What? Shouldn't be batted? Why not? I've made some and always used batting, they were made to be used. I, personally, love heavy quilts, probably because that was what I was raised with in cold, snowy WV. My DH learned to like being covered in cold weather with them or others, all heavy.

Tied and not machine quilted? Well, most likely that's because of all the "crazy" seams in it, might not look well, or work very well, but if that's what YOU want, go for it. At least give it a try. You might wind up way too familiar with Sammy Seam Ripper, but then you would know for sure.

Doesn't need to be bound? That doesn't sound right to me, because of all the different seam endings, I would want a padded seam binding on it. It's your quilt, no quilt police will come pounding on your door. I think you will love the finished quilt and will love it more as time goes by and friends and family complement you on it.