This is exactly what I was looking for.  It's a basic thin do-rag, with a lightweight headband.  Some do-rags have a thicker sweatband, which I do not like.  I find the thicker bands tend to accumulate sweat,which drips in my eyes.  As an added bonus, these are flat stitched, which was not the case with my old do-rags.  Overall I was impressed enough to retire all my old do-rags and replace them with these.  At the time I found these I was just trying to find something as good as what I had, but these turned out be even better.