  We give criteria of total incomparability for certain classes of mixed
Tsirelson spaces. We show that spaces of the form
$T[(M_k,\theta_k)_{k=1}^{\ell}]$ with index $i(M_k)$ finite are either $c_0$ or
$\ell_p$ saturated for some $p$ and we characterize when any two spaces of such
a form are totally incomparable in terms of the index $i(M_k)$ and the
parameter $\theta_k$. Also, we give sufficient conditions of total
incomparability for a particular class of spaces of the form
$T[(A_k,\theta_k)_{k=1}^\infty]$ in terms of the asymptotic behaviour of the
sequence $\Vert\sum_{i=1}^n e_i\Vert$ where $(e_i)$ is the canonical basis.
