  We report the first di-jet transverse momentum asymmetry measurements from
Au+Au and p+p collisions at RHIC. The two highest-energy back-to-back jets
reconstructed from fragments with transverse momenta above 2 GeV/c display a
significantly stronger momentum imbalance in heavy-ion collisions than in the
p+p reference. When re-examined with correlated soft particles included, we
observe that these di-jets then exhibit a unique new feature -- momentum
balance is restored to that observed in p+p for a jet resolution parameter of
R=0.4, while re-balancing is not attained with a smaller value of R=0.2.
