  We report an investigation of the self-energy screening effects for the $g$
factor of the ground state of Li-like ions. The leading screening contribution
of the relative order $1/Z$ is calculated to all orders in the binding nuclear
strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and
$\alpha$ is the fine-structure constant). We also extend the known results for
the $Z\alpha$ expansion of the QED screening correction by deriving the leading
logarithmic contribution of order $\alpha^5\ln\alpha$ and obtaining approximate
results for the $\alpha^5$ and $\alpha^6$ contributions. The comparison of the
two approaches yields a stringent check of consistency of the two calculations
and allows us to obtain improved estimations of the higher-order screening
effects.
