 A Euclidean disk that fills a circle can be replaced, without decreasing the distances between boundary points, by a Finsler disk that fills the same circle =10 times (in the sense that its boundary wraps around the circle times), but whose Holmes–Thompson area is less than times the area of the disk.For the hemisphere, a similar replacement can be found.In other words, the filling area conjecture is false if Finsler 2-chains with "rational coefficients" are allowed as fillings, instead of orientable surfaces (which can be considered as 2-chains with "integer coefficients").