We present results from an extensive study of 88 precessing , equal-mass black-hole binaries with large spins ( 83 with intrinsic spins | \vec { S } _ { i } / m _ { i } ^ { 2 } | of 0.8 and 5 with intrinsic spins of 0.9 ) , and use these data to model new nonlinear contributions to the gravitational recoil imparted to the merged black hole . We find a new effect , the cross kick , that enhances the recoil for partially aligned binaries beyond the hangup kick effect . This has the consequence of increasing the probabilities of recoils larger than 2000 km s ^ { -1 } by nearly a factor two , and , consequently , of black holes getting ejected from galaxies , as well as the observation of large differential redshifts/blueshifts in the cores of recently merged galaxies .