Think of the planes of this 'back end' of the swan - the 3D surfaces. Note how they meet in various lines. To clarify the forms for myself I made a third, quick model.
Remember the undercutting principle: Run the overlying form into the edge and get that right first. Only then are you safe to undercut
One of the issues with any carvers screw, which I am using here, is that mallet work in the 'unscrew' direction will of course unscrew it! Couple that with the screw's tapering end and the carving can become loose - in which case there's nothing else for it but to re-sink the screw and tighten the fly again. (But here's little trick: Insert a bit of non-slip matting under the carving...)