  Rational CFT's are classified by an integer $\ell$, the number of zeroes of
the Wronskian of their characters in moduli space. For $\ell=0$ they satisfy
non-singular modular-invariant differential equations, while for $\ell>0$ the
corresponding equations have singularities. We survey CFT's with two characters
and $\ell=0,2,3,4$ and verify the consistency, at the level of characters, of
some candidate theories with $\ell\ne 0$. For $\ell=2$ there are seven
consistents sets of characters. We identify specific combinations of level-1
current algebras that are potential symmetries of the corresponding CFT's.
