Tom... The Japanese have a form of that carving. They use it to carve a lot of their animals and dolls that they sell at the Temples and Festivals. Here is a just one sample of some Zodiac animals carved by a Facebook friend, Yasuhiro Ishibashi. If you look him up on Facebook you can view his entire collection and his other work.
These animals with this flat plane style have been called the origami style by some. I have been using this style to provide projects for the beginner carver that let them practice the basic knife cutting techniques. It's not long before these beginners can produce a nice whittling. It's also not long before some see this style and request something special to give a a gift.
Here's one such piece that was requested to give to a retired USMC officer.
Joyce, if you get concerned about carving something small, Leave a "handle" on the blank when cutting out the blank. I recommend leaving a 3 inch piece of wood attached to a foot. This piece can be a handle to hold the blank when carving, then cut off when the carving is completed.
I agree with Tom-H. When I was carving https://forum.woodcarvingillustrated...bottle-stopper I had pre-drilled the hole in the bottom that would have a dowel and cork. I took a piece of dowel and inserted it in the hole to give my holding hand something to grip while I was carving the rest. You can also make two carvings at once by leaving them joined; I did this with a pair of purpleheart earrings for my granddaughter - I left them joined at the tip of the hearts until the carving and most of the sanding was complete, then separated them. This gave me something to hold on to while carving...