The subject of the invention is a device for dispensing a cosmetic composition, comprising a dispensing head (1) intended to be fitted on a container containing said cosmetic composition to be dispensed,(i) the dispensing head comprising:a body (3) that is open at its two opposite axial ends,an engaging part (10) that is open at its two opposite axial ends and at least partially defines at least one dispensing orifice (12), the cross section of the dispensing orifice being between 0.05 mm2 and 0.5 mm2,(ii) the anhydrous cosmetic composition comprising, in a cosmetically acceptable medium,at least one oily phase comprising one or more oils chosen from silicone oils, hydrocarbon-based oils and fluoro oils,at least one cosmetic active agent, in particular at least one deodorant active agent and/or antiperspirant active agent.
