How do I sew jersey material without creating an overlap?

I have a black American Apparel sweatshirt that I was going to make into a penguin sweatshirt by cutting out the stomach and inside arms, bleaching them, and sewing them back on. I don't any overlap in the material because the pieces will fit perfectly and I don't want weirdness at the edge. Any tips?

You will want to finish the edges to prevent raveling, so zig-zag or serge the edges in the same color as your fabric. You may have luck using a variation on a French seam to put it back together.
French seam requires a separate piece of fabric - usually you sew the seam together as usual and then press it open, but here you would just butt the finished edges together on the separate piece of fabric and sew it down:
--x--,,--x-- ------------ Sew where the x is; the , indicates zig-zag edges - you might also want to zig-zag these together so the edges won't rumple.

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