  We consider the Dirichlet Laplacian $H_\gamma$ on a 3D twisted waveguide with
random Anderson-type twisting $\gamma$. We introduce the integrated density of
states $N_\gamma$ for the operator $H_\gamma$, and investigate the Lifshits
tails of $N_\gamma$, i.e. the asymptotic behavior of $N_\gamma(E)$ as $E
\downarrow \inf {\rm supp}\, dN_\gamma$. In particular, we study the dependence
of the Lifshits exponent on the decay rate of the single-site twisting at
infinity.
