  We have calculated the band-$f$ hybridizations for Ce$_x$La$_{1-x}$M$_3$
compounds ($x=1$ and $x\rightarrow 0$; M=Pb, In, Sn, Pd) within the local
density approximation and fed this into a non-crossing approximation for the
Anderson impurity model applied to both dilute and concentrated limits. Our
calculations produce crystalline electric field splittings and Kondo
temperatures with trends in good agreement with experiment and demonstrate the
need for detailed electronic structure information on hybridization to describe
the diverse behaviors of these Ce compounds.
