  We give a complete classification of mixed Tsirelson spaces T[(F\_i,
theta\_i)\_{i=1}^r ] for finitely many pairs of given compact and hereditary
families F\_i of finite sets of integers and 0<theta\_i<1 in terms of the
Cantor-Bendixson indexes of the families F\_i, and theta\_i (0< i < r+1). We
prove that there are unique countable ordinal alpha and 0<theta<1 such that
every block sequence of T[(F\_i, theta\_i)\_{i=1}^r ] has a subsequence
equivalent to a subsequence of the natural basis of the
T(S\_{omega^alpha},theta). Finally, we give a complete criterion of comparison
in between two of these mixed Tsirelson spaces.
