  We consider the simplicity of the $C^*$-algebra associated to a labelled
space $(E,\CL,\bE)$, where $(E,\CL)$ is a labelled graph and $\bE$ is the
smallest accommodating set containing all generalized vertices. We prove that
if $C^*(E, \CL, \bE)$ is simple, then $(E, \CL, \bE)$ is strongly cofinal, and
if, in addition, $\{v\}\in \bE$ for every vertex $v$, then $(E, \CL, \bE)$ is
disagreeable. It is observed that $C^*(E, \CL, \bE)$ is simple whenever $(E,
\CL, \bE)$ is strongly cofinal and disagreeable, which is recently known for
the $C^*$-algebra $C^*(E, \CL, \CEa)$ associated to a labelled space $(E, \CL,
\CEa)$ of the smallest accommodating set $\CEa$.
