We report here on an extension of a previous study by Kirsh et al. (Kirsh, D.R., Duncan, M., Brasser, R., Levison, H.F. . Icarus 199, 197-209) of planetesimal-driven migration using our N-body code SyMBA (Duncan, M.J., Levison, H.F., Lee, M.H. . Astron. J. 116, 2067-2077). The previous work focused on the case of a single planet of mass Mem, immersed in a planetesimal disk with a power-law surface density distribution and Rayleigh distributed eccentricities and inclinations. Typically 10 4-10 5 equal-mass planetesimals were used, where the gravitational force (and the back-reaction) on each planetesimal by the Sun and planet were included, while planetesimal-planetesimal interactions were neglected. The runs reported on here incorporate the dynamical effects of a gas disk, where the Adachi et al. (Adachi, I., Hayashi, C., Nakazawa, K. . Prog. Theor. Phys. 56, 1756-1771) prescription of aerodynamic gas drag is implemented for all bodies. In some cases the Papaloizou and Larwood (Papaloizou, J.C.B., Larwood, J.D. . Mon. Not. R. Astron. Soc. 315, 823-833) prescription of Type-I migration for the planet are implemented, as well as a mass distribution. In the gas-free cases, rapid planet migration was observed - at a rate independent of the planet's mass - provided the planet's mass was not large compared to the mass in planetesimals capable of entering its Hill sphere. In such cases, both inward and outward migrations can be self-sustaining, but there is a strong propensity for inward migration. When a gas disk is present, aerodynamic drag can substantially modify the dynamics of scattered planetesimals. For sufficiently large or small mono-dispersed planetesimals, the planet typically migrates inward. However, for a range of plausible planetesimal sizes (i.e. 0.5-5.0 km at 5.0 AU in a minimum mass Hayashi disk) outward migration is usually triggered, often accompanied by substantial planetary mass accretion. The origins of this behaviour are explained in terms of a toy model. The effects of including a size distribution and torques associated with Type-I migration are also discussed.