  Available analyses on moments of the spin structure function g_1 use
different methods and are barely consistent with each other. We present a
higher twist analysis of Gamma_1^p using a method consistent with the studies
of Gamma_1^n and Gamma_1^(p-n) already published. The twist-4 coefficient f_2
is extracted. One result is that the higher twist coefficients seem to
alternate signs: the relatively larger twist-6 contribution is partly
suppressed by the twist-4 and twist-8 contributions. The size of twist-6 can be
due to the elastic contribution to the moments.
