Hi Pilou, can you please post the file?

You should use the "Refit to tolerance" option if you want to get the minimal amount of control points on a wide selection of curves.

That will fit a line with 2 control points and a curve will be fit with more control points in curvy areas and less control points in flat areas.

If you want the minimal number of control points, then use that mode and not the "number of points" mode, because the number of points mode will just use exactly the number of points that you tell it.

- Michael