vocals: to tune, or not to tune?

I comp the piss out of vocals first before spanking them with tuning software.
But for natural tuning, i prefer melodyne
 
Autotune in graphic mode or melodyne

if she's really that good that it even wasnt that audible during recording then you shouldnt have problems tuning only those parts that are a bit off, without making it sounding unnatural.
just edit those parts that need it. you dont even need to snap it 100% on the grid, just experient were it sounds good and leave it at that.

When singers are REALLY good you sometimes have the problem that some notes sound extremely off, because they are THAT accurate normally.
so when you open up the pitch correction and analyze it you see that its not even that much off, but its a lot more audible because the rest is so perfect...if that makes sense?
at least that was the experience with my bands singer.
 
just curious: why does it sound better to tune small bits or note for note?
i thought the 'correct pitch' macro with which you can tune the entire track was the same?

Because them you can shape the pitch curve exactly how you want. By tuning the whole track at once, sometimes Melodyne screws up some stuff that will only sound nice when chopping the word in smaller pieces.

I actually use the 'auto' tuning of Melodyne just to correct the center of the notes and then go back correcting the screw ups and the word with too much vibrato and stuff. If the vocal is not terrible, you can manage to get very real results by using this method.