I have an old pipe here, my buddy gave it to me back in the 70's, not sure of the make.  Smaller bowl, I like that size, great for quick smokes and I'm not a confirmed pipe smoker, sometimes only one bowl per month.  Anyways, this little pipe has a "squashed" bowl, like you put the bowl in a vise and tightened it from both sides.  The top opening is quite oval in shape, never seen one like it and not sure what the shape would be.  Maybe a squashed billiard or something like that?  Wish I could post a photo but I'm not at that level yet.

Sounds to me like a (Tomato )Oval squashed fits nicely in your hand? Your apples tend to be more round.

here's some good references.  Note that there is no industry standard for pipe shapes....companies can call a pipe anything they want.  My guess is you are describing a "prince".



http://www.theitalianpipe.com/infowell/shapes.htm



http://members.bellatlantic.net/~vze43wza/smoke/shape.html

Sounds more like the Square Panel shape, because it appears pressed from the *sides* not top and bottom and the bowl is oval:

"... this little pipe has a "squashed" bowl, like you put the bowl in a vise and tightened it from both sides. The top opening is quite oval in shape ..."

Does it have a filter?  If yes, given the info, I'd say it's a Medico.

Does it have a Spades (the symbol from playing cards) on the stem?  It could be a Dr. Grabow -- they got real artsy-fartsy with pipe shapes in the 70's.