E string fret buzz

I bought a cheap bass, an 'Artist' brand. I am not generally a brand follower and this time I lucked out; I would have no hesitation gigging this inexpensive instrument if it wasn't for one problem: There is a persistent buzz on the E string. It sounds like a fret buzz but I have set the truss rod and prefer a moderate to higher action. To get a good clean note on this string I have to fret right up behind the fret and quite firmly. any ideas what could be causing this?