An anhydrous hydrophobic cosmetic composition in the form of a compact powder which can be taken up in dry form or with water, comprising a particulate phase comprising hydrophilic pulverulent compounds, wherein the hydrophilic pulverulent compounds represent 20 to 35% by weight relative to the total weight of the particulate phase. The invention also relates to a make-up process using such a composition, as well as to a device comprising such a composition and a sponge which can be moistened.