Thank you - I have been "fighting" with my D string for the last 3 hours, trying to figure out where this comes from. I used new Hannabach (black, medium tension) and the buzz was quite strong on the 2nd, 3rd and 4th frets. So I tried to use some shims (paper) under the nut to increase the height of the strings, and it helped a bit, but the buzz never disappeared.
Before, I had red Savarez on the guitar and did not notice this buzzing at all.
The guitar (a Picado 60) is in great shape, no problems with the frets or the neck, as fas as I can see. Also the saddle is high enough, and the height of the strings at the 12 fret is normal, certainly not too low. So I suspected it was something with the new strings but had no idea what.
So, I replaced the D string with a new hard-tension (d'Addario) string and it was immedately much better.