Suppose that (F_n)_{n=0}^{infty} is a sequence of regular families of finite subsets of N such that F_0 contains all singletons, and (theta _n)_{n=1}^{infty} is a nonincreasing null sequence in (0,1). In this paper, we compute the Bourgain ell^1 - index of the mixed Tsirelson space T(F_0,(theta_n, F_n)_{n=1}^{infty}). As a consequence, it is shown that if eta is a countable ordinal not of the form omega^xi for some limit ordinal xi, then there is a Banach space whose ell^1-index is omega^eta . This answers a question of Judd and Odell.
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