Peckish

I mean exactly that - don't press it in half (lengthwise). Just fold it, align the raw edges with the raw edge of the quilt, and sew it on, just as you normally would.

Think about a running track. The inner lane of the track is not as long as the outer lane of the track, correct? Now envision your binding as the track, going around the edge of the quilt. The inner part of the binding is going to be shorter than the outer part, and ironing a crease in it doesn't allow the fabric to adjust. If you don't press it, the fabric is free to shift and adjust to best fit around that U curve. It seems like a very small thing, but the width of a couple of threads makes a huge difference. That's why we use a "scant" quarter inch seam, right? If you don't press your binding, it will lay much nicer, flatter, and fuller on the edge of the quilt.