I love skinny bindings, especially on wall quilts. One thing to remember though is that the skinnier the binding, the more likely any inconsistency will be obvious.
For this wallhanging with its repeated small in and out curves, a single layer binding finishing just under 1/4" and handstitched on the back worked best.
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This bed quilt had gentler curves, which allowed me to use a slightly wider binding and finish by stitching in the ditch from the front, catching the binding edge on the reverse side. This is my usual way of binding.
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I wanted to finish my latest wall quilt by the same method, but fabric available for cutting the binding was so scant that I ended up cutting 1-3/4" strips and handstitching on the back.
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Daffy