  We revisit Bondi accretion - steady-state, adiabatic, spherical gas flow onto
a Schwarzschild black hole at rest in an asymptotically homogeneous medium -
for stiff polytropic equations of state (EOSs) with adiabatic indices $\Gamma >
5/3$. A general relativistic treatment is required to determine their accretion
rates, for which we provide exact expressions. We discuss several qualitative
differences between results for soft and stiff EOSs - including the appearance
of a minimum steady-state accretion rate for EOSs with $\Gamma \geq 5/3$ - and
explore limiting cases in order to examine these differences. As an example we
highlight results for $\Gamma = 2$, which is often used in numerical
simulations to model the EOS of neutron stars. We also discuss a special case
with this index, the ultra-relativistic `causal' EOS, $P = \rho$. The latter
serves as a useful limit for the still undetermined neutron-star EOS above
nuclear density. The results are useful, for example, to estimate the accretion
rate onto a mini-black hole residing at the center of a neutron star.
