  We consider classical Tsirelson-type norms of $T[A_r,\theta]$ and their
modified versions on $\ell_p$ spaces. We show that for any $1<p<\infty$ there
is a constant $\lambda_p$ such that considered Tsirelson-type norms do not
$\lambda_p$-distort any of subspaces of $\ell_p$.
