  A well known argument of James yields that if a Banach space $X$ contains
$\ell_1^n$'s uniformly then $X$ contains $\ell_1^n$'s almost isometrically. In
the first half of the paper we extend this idea to the ordinal $\ell_1$-indices
of Bourgain. In the second half we use our results to calculate the
$\ell_1$-index of certain Banach spaces. Furthermore we show that the
$\ell_1$-index of a separable Banach space not containing $\ell_1$ must be of
the form $\omega^{\alpha}$ for some countable ordinal $\alpha$.
