Tsirelson's space T is known to be distortable but it is open as to whether
or not T is arbitrarily distortable. For n is an element of N the norm par
allel to . parallel to(n) of the Tsirelson space T(S-n, 2(-n)) is equivalen
t to the standard norm on T. We prove there exists K < infinity so that for
all n, parallel to . parallel to, does not K distort any subspace Y of T.