If you leave too little, you will not get sufficient carbonation. If you leave too much, you'll likely get overcarbonation.
With that said, IowaStateFan, do you REALLY fill to within an inch of the top, or are you just guessing? Commercial beers are often 2"-2.5" of headspace, and I wouldn't say I fill DRASTICALLY more than they do. I just ran a simple test, filling a bottle and standard bottling wand (with gravity valve) with water, and when I removed the wand there was 1.75" of head space. That's a pretty significant difference from the 1" you have quoted - if you are actually filling to within 1" of the top, I would say you are overfilling.
For example, the bottles in this picture are filled about the same as the one I just ran the test with, and should be around 1.75" headspace:
https://cdn.homebrewtalk.com/gallery/showimage.php?i=4175&catid=searchresults&searchid=1888
And unless someone disagrees, I'd say those are properly filled.