It's interesting to think about what relief (concave) does.
For a given amount of action at the twelfth fret, relief makes minimal impact on the frets near the 12th fret.
As you move along the neck towards the nut, the action reduces more slowly than with a flat neck. This reduces buzzing on the lower notes and compensates for the longer the causing greater excursion (the amount the string moves back and forth).
As you move beyond the twelfth fret, the action reduces more rapidly than with a flat fretboard. However, the extra stiffness around the neck joint makes this a less significant amount and the rapidly reducing excursion of the strings means this shouldn't be a big issue.
Buzzing occurs when either the next fret (or rarely the next but one) is high, or a fret is low. The differences are often on the scale of a thousandth of an inch or even less.
Assuming that the frets are decently levelled, buzzing on the higher notes usually means that there is too much neck relief (or there's a 'ski jump' as mentioned earlier). This is particularly likely if buzzing happens in multiple places.
Similarly, buzzing on low notes (not open strings, which is a poorly cut nut) means too little or convex neck relief.
One way of getting very low action is to set up the bass, then add a little more truss rod tension which will reduce the action by a 'smidgin' but barely affect the string angles on the highest frets. If this does cause a buzz on low notes, put the relief back on. In most cases it will be OK or a little buzz close higher than the 12th fret. In this case you may need to slightly raise one or two saddles, but should still end up with lower action than before.