  Recently, the quantum spin-Hall edge channels of two-dimensional colloidal
nanocrystals of the topological insulator Bi$_2$Se$_3$ were observed directly.
Motivated by this development, we reconsider the four-band effective model
which has been traditionally employed in the past to describe thin nanosheets
of this material. Derived from a three-dimensional $\boldsymbol{k}
\boldsymbol{\cdot} \boldsymbol{p}$ model, it physically describes the top and
bottom electronic surface states at the $\Gamma$ point that become gapped due
to the material's small thickness. However, we find that the four-band model
for the surface states alone, as derived directly from the three-dimensional
theory, is inadequate for the description of thin films of a few quintuple
layers and even yields an incorrect topological invariant within a significant
range of thicknesses. To address this limitation we propose an eight-band model
which, in addition to the surface states, also incorporates the set of bulk
states closest to the Fermi level. We find that the eight-band model not only
captures most of the experimental observations, but also agrees with previous
first-principles calculations of the $\mathbb{Z}_{2}$ invariant in thin films
of varying thickness. The band inversion around the $\Gamma$ point, which
endows the surface-like bands with topology, is shown to be enabled by the
presence of the additional bulk-like states without requiring any
reparametrization of the resulting effective Hamiltonian.
