These elastic corsets are both from True Grace Corsets (TGC). They are elastic above and below the waist. At the waist there is a rigid band which produces the necessary pressure to form the waist.

I had an elastic corset from Michael Garrod with a minimum laced waistline of 17 inch. An elastic corset is not very durable. After one to two years the rubber material will be worn out and thus will no longer be suitable to form the body.