As I am working on being a nitpicky malcontent--it is in my best interests to make a fuss about every little thing--otherwise I wouldn't have even mentioned any of this--but seriously--

When you can drop a note or two out of a chord, it can give you a lot of extra room to work, and this is really important, because it helps to overcome the limitations inherent in the guitar--it is good to know, however, that when you drop the fundamental out of a C9, you are really playing an Em7-5 or Gm6--this is important especially when you are working with non-guitar instumentalists--the chord sounds may be significantly altered when a note is dropped, because a whole different array of harmonics are sounding--you can go from a very straight ahead sound to a really bent one, and this is sometimes not appreciated, especially by Traditional Jazz ensembles--

(then of course, you may also run into that occasional bass player who "hears" it as an E or G chord, and decides to stick the fifth on the bottom)

Also, you have to be careful about which notes you add and leave out if you are working with a vocalist, because they often rely on the guitar chords to lead them--

I once copped a particularly hip set of changes to "Pennies from Heaven" from a jazz pianist, only to discover that it left my vocalist singing a B over a C7 chord--and he did not like it, not one little bit--and pulled the sheet music out to show me that I was wrong--went back to the pianist will this problem, and he said, "It may be a little out there, but it's close enough for Jazz"

Anyway, the third and the seventh tend are the really important notes in defining a chord--