[en] The ratio of total mass $m_{\ast <!--\; ???\; -->}$ to the surface radius $r_{\ast <!--\; ???\; -->}$ of a spherical perfect fluid ball has an upper bound, ${Gm}_{\ast <!--\; ???\; -->}/(c^2{r}_{\ast <!--\; ???\; -->})⩽<!--\; ???\; -->\mathcal{B}.$ Buchdahl (1959 Phys. Rev. 116 1027) obtained the value ${\mathcal{B}}_{\mathrm{B}\mathrm{u}\mathrm{c}\mathrm{h}}=4/9$ under the assumptions that the object has a nonincreasing mass density in the outward direction and a barotropic equation of state. Barraco and Hamity (2002 Phys. Rev. D 65 124028) decreased Buchdahl's bound to a lower value, ${\mathcal{B}}_{\mathrm{B}\mathrm{a}\mathrm{H}\mathrm{a}}$ = 3/8 (<4/9), by adding the dominant energy condition to Buchdahl's assumptions. In this paper, we further decrease Barraco–Hamity's bound to ${\mathcal{B}}_{\mathrm{n}\mathrm{e}\mathrm{w}}\simeq <!--\; ???\; -->0.3636403$ (<3/8) by adding the subluminal (slower than light) condition of sound speed. In our analysis we numerically solve the Tolman–Oppenheimer–Volkoff equations, and the mass-to-radius ratio is maximized by variation of mass, radius and pressure inside the fluid ball as functions of mass density. (paper)