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coutil

n. A woven cloth created specifically for making corsets.

Wikipedia
Coutil

Coutil (or Coutille) is woven cloth created specifically for making corsets. It is woven tightly to inhibit penetration of the corset's bones and resist stretching. Coutil has a high cotton content. Cotton has good dimensional stability, or a resistance to stretching, which makes it a good choice for such a stressed garment. Coutil may be made to be plain (similar to 100% cotton facing), satin, or brocade. It is common for coutil to have a herringbone texture, or a similar woven texture.