  We explore the diversity of subsymmetric basic sequences in spaces with a
subsymmetric basis. We prove that the subsymmetrization $Su(T^*)$ of
Tsirelson's original Banach space provides the first known example of a space
with a unique subsymmetric basic sequence that is additionally non-symmetric.
Contrastingly, we provide a criterion for a space with a subsymmetric basis to
contain a continuum of nonequivalent subsymmetric basic sequences and apply it
to $Su(T^*)^*$. Finally, we provide a criterion for a subsymmetric sequence to
be equivalent to the unit vector basis of some $\ell_p$ or $c_0$.
