Upper bound on the gravitational masses of stable spatially regular charged compact objects

In a very interesting paper, Andr'easson has recently proved that the gravitational mass of a spherically symmetric compact object of radius $R$ and electric charge $Q$ is bounded from above by the relation $\sqrt{M}\le \frac{\sqrt{R}}{3}+\sqrt{\frac{R}{9}+\frac{Q^2}{3R}}$. In the present paper we prove that, in the dimensionless regime $Q\mathrm{/}M<\sqrt{9\mathrm{/}8}$, a stronger upper bound can be derived on the masses of physically realistic ({\it stable}) self-gravitating horizonless compact objects: $M<\frac{R}{3}+\frac{2Q^2}{3R}$.