The form of fields in a conical horn with uniform circumferential corrugations, when the corrugation depth assumes arbitrary values in the interval 0.25 ≦ (h/γo0) ≦ 0.5 is investigated in this paper. Assuming the corrugations to be infinitely thin and sufficiently close-packed, an impedance boundary condition is imposed on the fields in the axial region. Subject to a far-field approximation, accurate expressions are derived for the aperture field through a hybrid-mode formalism, which are subsequently used to calculate numerically the diffracted far-field of the horn supporting the HE11mode, using Silver's formula. Satisfactory agreement between calculated and measured values of the far-field pattern for a wide-flare horn having arbitrary values ofh/γosupports the validity of the theory presented. When the half-flare angle (α2:) is less than 30°, a closed form expression is derived for the on-axis gain of the horn.