  Let f be a cusp form for the group SL(3, Z) with Langlands parameter mu and
associated L-function L(s, f). If mu is in generic position, i.e. away from the
Weyl chamber walls and away from the self-dual forms, we prove the subconvexity
bound L(1/2, f) << || mu || ^{3/4 - 1/120000}.
