I find that even when my Strat is properly tuned and intonated, some open chords sound pretty bad. It seems to be a problem with notes fretted at the first few frets -- especially on the lower strings. Open E, open G, etc.
If I'm really careful and only press the strings down enough to fret them -- but not far enough to actually touch the fretboard -- then they're on pitch. But pressing them down to the fretboard brings them just sharp enough to be annoying.
Is this a problem with the nut, or the first few frets, or both? What can I do about it?