Black yarn

I have dyed black yarn before, but I have never dyed cotton black before. The last time that I dyed yarn black I was dyeing silk. It took three dye baths, but I got that nice inky black color. This stuff is coming out a kind of dark grey/faded black. Some turned out pretty good, but not inky black. That yarn started out grey that I dyed black before. It wasn't black enough. I am weaving black and red, and it is turning out not too bad. The red is kind of making the black blend in as I am weaving with about three or four shades of black, none of them that nice inky black.