Eddie, assuming the action is not too low, causing buzzing, the effect you describe is usually the result of the guitar string not resting squarely on the top nut (by 1st fret) or at the bridge end. This results in a tiny part of the string buzzing very slightly against the top nut.
Using very light gauge strings can contribute to the problem if the string groove was cut to suit thicker strings. The string buzzes in its groove instead of creating a clear sound.
If the string is thicker than the groove it could be resting on top of the groove instead of running through it. This can cause the same effect.
If the string is running across the tuning peg side of the top nut instead of resting firmly on the fingerboard side, angle the string groove down slightly towards the tuning side using a thin-bladed serrated kitchen knife in a sawing motion. Be careful!
Sorry I can't fit a diagram in to make it easier, but I hope this helps.
Les Herridge
November 2007