  Let $G$ be an algebraic group of classical type of rank $l$ over an
algebraically closed field $K$ of characteristic $p$. We list and determine the
dimensions of all irreducible $KG$-modules $L$ with $\dim L < \binom{l+1}{4}$
if $G$ is of type $A_l$, and with $\dim L < 16 \binom{l}{4}$, if $G$ is of type
$B_l$, $C_l$ or $D_l$.
