  We obtain first-order equations for G_2 holonomy of a wide class of metrics
with S^3\times S^3 principal orbits and SU(2)\times SU(2) isometry, using a
method recently introduced by Hitchin. The new construction extends previous
results, and encompasses all previously-obtained first-order systems for such
metrics. We also study various group contractions of the principal orbits,
focusing on cases where one of the S^3 factors is subjected to an Abelian,
Heisenberg or Euclidean-group contraction. In the Abelian contraction, we
recover some recently-constructed G_2 metrics with S^3\times T^3 principal
orbits. We obtain explicit solutions of these contracted equations in cases
where there is an additional U(1) isometry. We also demonstrate that the only
solutions of the full system with S^3\times T^3 principal orbits that are
complete and non-singular are either flat R^4 times T^3, or else the direct
product of Eguchi-Hanson and T^3, which is asymptotic to R^4/Z_2\times T^3.
These examples are in accord with a general discussion of isometric fibrations
by tori which, as we show, in general split off as direct products. We also
give some (incomplete) examples of fibrations of G_2 manifolds by associative
3-tori with either T^4 or K3 as base.
