A kit comprising a device for dispensing an anhydrous composition and said anhydrous composition comprised in the device: i) the device comprising a dispensing head intended to be fitted on a container that contains said composition, comprising: - a body that is open at its two opposite axial ends, - an engaging part that is open at its two opposite axial ends, at least partially defining at least one dispensing orifice, the sum of the cross section(s) of the dispensing orifice(s) being between 0.02 mm2 and 0.5 mm2, ii) the anhydrous composition comprising, in particular in a physiologically acceptable medium: a) at least one oily phase comprising at least one volatile hydrocarbon-based oil, and b) at least one clay, and c) at least one deodorant active agent, and d) at least one propellant characterized in that: said at least one volatile hydrocarbon-based oil is selected from C8-C16 isoalkanes and in particular from isododecane, isodecane, isohexadecane and mixtures thereof, and more particularly still isododecane, and said clay is selected from hydrophobic modified bentonites and hydrophobic modified hectorites, in particular that are modified by a C10 to C22 quaternary ammonium chloride, and more particularly selected from bentonites modified by stearalkonium chloride and hectorites modified by distearyldimethylammonium chloride. i) the device comprising a dispensing head intended to be fitted on a container that contains said composition, comprising: - a body that is open at its two opposite axial ends, - an engaging part that is open at its two opposite axial ends, at least partially defining at least one dispensing orifice, the sum of the cross section(s) of the dispensing orifice(s) being between 0.02 mm2 and 0.5 mm2, - a body that is open at its two opposite axial ends, - an engaging part that is open at its two opposite axial ends, at least partially defining at least one dispensing orifice, the sum of the cross section(s) of the dispensing orifice(s) being between 0.02 mm2 and 0.5 mm2, ii) the anhydrous composition comprising, in particular in a physiologically acceptable medium: a) at least one oily phase comprising at least one volatile hydrocarbon-based oil, and b) at least one clay, and c) at least one deodorant active agent, and d) at least one propellant characterized in that: said at least one volatile hydrocarbon-based oil is selected from C8-C16 isoalkanes and in particular from isododecane, isodecane, isohexadecane and mixtures thereof, and more particularly still isododecane, and said clay is selected from hydrophobic modified bentonites and hydrophobic modified hectorites, in particular that are modified by a C10 to C22 quaternary ammonium chloride, and more particularly selected from bentonites modified by stearalkonium chloride and hectorites modified by distearyldimethylammonium chloride. a) at least one oily phase comprising at least one volatile hydrocarbon-based oil, and b) at least one clay, and c) at least one deodorant active agent, and d) at least one propellant said at least one volatile hydrocarbon-based oil is selected from C8-C16 isoalkanes and in particular from isododecane, isodecane, isohexadecane and mixtures thereof, and more particularly still isododecane, and said clay is selected from hydrophobic modified bentonites and hydrophobic modified hectorites, in particular that are modified by a C10 to C22 quaternary ammonium chloride, and more particularly selected from bentonites modified by stearalkonium chloride and hectorites modified by distearyldimethylammonium chloride.