  We study a class of ${\cal N}=(1,0)$ little string theories obtained from
orbifolds of M-brane configurations. These are realised in two different ways
that are dual to each other: either as $M$ parallel M5-branes probing a
transverse $A_{N-1}$ singularity or $N$ M5-branes probing an $A_{M-1}$
singularity. These backgrounds can further be dualised into toric, non-compact
Calabi-Yau threefolds $X_{N,M}$ which have double elliptic fibrations and thus
give a natural geometric description of T-duality of the little string
theories. The little string partition functions are captured by the topological
string partition function of $X_{N,M}$. We analyse in detail the free energies
$\Sigma_{N,M}$ associated with the latter in a special region in the K\"ahler
moduli space of $X_{N,M}$ and discover a remarkable property: in the
Nekrasov-Shatashvili-limit, $\Sigma_{N,M}$ is identical to $NM$ times
$\Sigma_{1,1}$. This entails that the BPS degeneracies for any $(N,M)$ can
uniquely be reconstructed from the $(N,M)=(1,1)$ configuration, a property we
refer to as self-similarity. Moreover, as $\Sigma_{1,1}$ is known to display a
number of recursive structures, BPS degeneracies of little string
configurations for arbitrary $(N,M)$ as well acquire additional symmetries.
These symmetries suggest that in this special region the two little string
theories described above are self-dual under T-duality.
