  The ratio of total mass $M$ to surface radius $R$ of spherical perfect fluid
ball has an upper bound, $M/R < B$. Buchdahl obtained $B = 4/9$ under the
assumptions; non-increasing mass density in outward direction, and barotropic
equation of states. Barraco and Hamity decreased the Buchdahl's bound to a
lower value $B = 3/8$ $(< 4/9)$ by adding the dominant energy condition to
Buchdahl's assumptions. In this paper, we further decrease the Barraco-Hamity's
bound to $B \simeq 0.3636403$ $(< 3/8)$ by adding the subluminal
(slower-than-light) condition of sound speed. In our analysis, we solve
numerically 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.
