  We investigate the Bethe-Ansatz (BA) approach to the superconformal index of
${\cal N}=4$ supersymmetric Yang-Mills with SU($N$) gauge group in the context
of finite rank, $N$. We explicitly explore the role of the various types of
solutions to the Bethe-Ansatz Equations (BAE) in recovering the exact index for
$N=2,3$. We classify the BAE solutions as standard (corresponding to a freely
acting orbifold $T^2/\mathbb{Z}_m \times \mathbb{Z}_n$) and non-standard. For
$N=2$, we find that the index is fully recovered by standard solutions and
displays an interesting pattern of cancellations. However, for $N\ge 3$, the
standard solutions alone do not suffice to reconstruct the index. We present
quantitative arguments in various regimes of fugacities that highlight the
challenging role played by the continuous families of non-standard solutions.
