Hey Becky, the best way is to make sure you bulk up your puppet with balsa wood, styrofoam or wadded up aluminum foil . Then build up the rest with clay - assuming your puppet will be clay in the end. I guess it depends on how you're making the puppet and the materials. If you can give more details I can give you more ideas.

Hi Becky, ok so it is clay contruction. In that case, you may try to epoxy a ping pong ball or other hollow object inside the head. Or if it's possible you could hollow out the head you made already and then try to insert pieces of styrofoam, wadded paper or aluminum foil. Then close the head back up with clay over the top.

I've done this in the past and it helps, but if this doesn't your armature might need to be made stonger. It would require major surgery if you have clay already over it. But an extra twist or strand of wire in the legs that you tie to the existing armature will usually help a lot too.