This talk describes a theoretical study of giant planet migration in the presence of both disk torques and scattering from other planets. These dynamical systems are highly chaotic and the results must be presented in terms of the distributions of possible orbital elements; we thus undertake a statistically comprehensive study of this migration mechanism. During the planet formation epoch, both residual circumstellar disks and multiple planets are expected to be present. Disk torques and planet-planet scattering change the orbital elements of migrating planets in complementary ways. Disks are effective at moving planets inward (changing the semi-major axes $a$), whereas planet-planet scattering is effective at increasing the orbital eccentricities $e$. The interplay between these two effects leads to a wide variety of possible outcomes. We show that this model -- migration driven by tidal interactions with a disk and by dynamical scattering from other planets -- naturally produces the observed range of semi-major axis and eccentricity.