  We extend existing results that characterize isometries on the Tsirelson-type
spaces $T\big[\frac{1}{n}, \mathcal{S}_1\big]$ ($n\in \mathbb{N}, n\geq 2$) to
the class $T[\theta, \mathcal{S}_{\alpha}]$ ($\theta \in \big(0,
\frac{1}{2}\big]$, $1\leqslant \alpha < \omega_1$), where
$\mathcal{S}_{\alpha}$ denote the Schreier families of order $\alpha$.
  We prove that every isometry on $T[\theta, \mathcal{S}_1]$ ($\theta \in
\big(0, \frac{1}{2}\big]$) is determined by a permutation of the first $\lceil
{\theta}^{-1} \rceil$ elements of the canonical unit basis followed by a
possible sign-change of the corresponding coordinates together with a
sign-change of the remaining coordinates. Moreover, we show that for the spaces
$T[\theta, \mathcal{S}_{\alpha}]$ ($\theta \in \big(0, \frac{1}{2}\big]$,
$2\leqslant \alpha < \omega_1$) the isometries exhibit a more rigid character,
namely, they are all implemented by a sign-change operation of the vector
coordinates.
