  In view of recent experimental progress in rate and CP asymmetry measurements
in $B^{\pm} \to DK^{\pm}$, we reconsider information on the weak phase $\gamma$
which can be obtained from these processes. Model-independent inequalities are
proven for $\sin^2\gamma$ in terms of two ratios of partial rates for
$B^{\pm,0} \to D X_s^{\pm,0}$, where $X_s$ is any multiparticle charmless state
carrying strangeness $\pm 1$. Good prospects are shown to exist for using these
inequalities and CP asymmetry measurements in two body and multibody decays in
order to improve present bounds on $\gamma$.
