What do you mean by sediments? it depends on the French Press and the grind size. I can get a sludge-free coffee with the Espro Press that still has a much fuller body than a filtered coffee due to the oils etc. If the grind size gets too fine, I get some sludge. Generally, sludge can be reduced by removing the white-ish foam. Or so I've heard; I've never used a Bodum french press (or similar), just an Espro Press.