  Isothermic surfaces in $S^n$ are characterised by the existence of a pencil
$\nabla^t$ of flat connections. Such a surface is special of type $d$ if there
is a family $p(t)$ of $\nabla^t$-parallel sections whose dependence on the
spectral parameter $t$ is polynomial of degree $d$. We prove that any
isothermic surface admits a family of $\nabla^t$-parallel sections which is a
formal Laurent series in $t$. As an application, we give conformally invariant
conditions for an isothermic surface in $S^3$ to be special.
