Editing curves on surfaces

When I try to edit points of a curve on a surface or polysurface, I use snaps to keep the control points of the curve snapped to the surface. But even though the curve’s control point stays on the surface, the curve itself comes off the surface a little bit. How can I edit the curves using their control points, but keep the curves precisely on the surface?

Hi Amy - try Project of a planar curve or Pull of a curve that is already close to a curved surface, using History. The projected or pulled curves will be within tolerance of the surface, and you can edit them by editing the points on the originals.