In this article, we present a theory for the dielectric behavior of a colloidal spheroid, based on an improved version of a previously published analytical theory [C. Chassagne, D. Bedeaux, G.J.M. Koper, Physica A 317 (2003) 321-344]. The theory gives the dipolar coefficient of a dielectric spheroid in an electrolyte solution subjected to an oscillating electric field. In the special case of the sphere, this theory is shown to agree rather satisfactorily with the numerical solutions obtained by a code based on DeLacey and White's [E.H.B. DeLacey, L.R. White, J. Chem. Soc. Faraday Trans. 2 77 (1981) 2007] for all zeta potentials, frequencies and kappa a1 where kappa is the inverse of the Debye length and a is the radius of the sphere. Using the form of the analytical solution for a sphere we were able to derive a formula for the dipolar coefficient of a spheroid for all zeta potentials, frequencies and kappa a1. The expression we find is simpler and has a more general validity than the analytical expression proposed by O'Brien and Ward [R.W. O'Brien, D.N. Ward, J. Colloid Interface Sci. 121 (1988) 402] which is valid for kappa a >> 1 and zero frequency.