In the watch world I grew up in...the pocket watch world, "rare" meant 1-5 or 1-10 ever made. It did not mean anything about desirability or valuable. It meant only the quantity. I remember when a popular watch guide book came out with their "Star Rarity Rating" a lot of the old codgers went nuts because it meant that watches they considered only scarce were being called rare. Here is that rating:

***** (five star) ............. RARE 1-25 produced
**** (four star) ............ SCARCE <100
*** (three star) .......... VERY FEW <350
** (two star) ............ SPARCE <1,000
* (one star) ........... UNCOMMON <2,500

This book also has a condition rating which describes NOS as "PRISTINE MINT"...(G-10) NOS, Absolutely factory new; unused in factory box with all paper still intact and all tags and papers etc. They go on to describe a total of 4 different states of MINT from the PRISTINE MINT to MINT PLUS to MINT to NEAR MINT.

I suppose I am OK with "rare" meaning anything from 1-5 to 1-25 produced but I am afraid that any of these do not allow for your criteria #3.

Your Asshole Friend
Little Johnny