A cartridge with a composite cartridge case includes a projectile with an ogee-shaped tip and a bottom end ending in a base, a flangeless tubular case delimiting a chamber accommodating a propulsive powder, closed at a first longitudinal end by a base with a primer and at the second end opposite to the first, by the base of the projectile, a part of the flangeless tubular case fitting snugly around part of the projectile and having itself, at least in part, a frustoconical external shape, the cartridge being characterized in that: —the chamber accommodating the propulsive powder includes, at the projectile end, a reduction in its diameter over all or part of the periphery thereof down to the diameter of the base of the projectile, —the ratio between the length of the tip of the projectile and the maximum diameter thereof is greater than or equal to 2.9.