  Using the self-dual lattice method, we make a systematic search for modular
invariant partition functions of the affine algebras $g\*{(1)}$ of $g=A_2$,
$A_1+A_1$, $G_2$, and $C_2$. Unlike previous computer searches, this method is
necessarily complete. We succeed in finding all physical invariants for $A_2$
at levels $\le 32$, for $G_2$ at levels $\le 31$, for $C_2$ at levels $\le 26$,
and for $A_1+A_1$ at levels $k_1=k_2\le 21$. This work thus completes a recent
$A_2$ classification proof, where the levels $k=3,5,6,9,12,15,21$ had been left
out. We also compute the dimension of the (Weyl-folded) commutant for these
algebras and levels.
