I understand what you mean. These "egg" or "crescent", (or as I call them "freestyle" pots) are my very first attempts to construct this sytle. (I made them for a friend who posts on this forum). I have learned alot about making pots like this.
The "second generation" of freestyle pots I am making now have several improvements. The walls of the pot, rise from the base almost vertically, rather than being inclined outward. And I have cut channels on the base, between the wiring holes so the pot will sit flat. These channels provide a place for the wire or twine, to be recessed.
I am also messing around with colored slips. The very dark pot (with the weird ring base) was made using a colored slip, bisqued fired, then an oxide wash was applied.
thank you all for the feedback (especially Tachigi, who I was able to chat with directly and share several other pictures in a chatroom. I am happy to say that my pottery "eye" has been increased thru his knowledge and advice. Many other people have influenced the direction I am heading)