The peculiar relationship of Pluto to Neptune, its resonances and high eccentricity and inclination, have led to the theory that the relationship arose from the migration of the outer planets, particularly the outward migration of Neptune, during the early solar system. In support of this scenario is the fact that the formation of Neptune at its current location would have been complicated by long dynamical times and low densities in the solar nebula. Here we address the following questions: Though the formation of Neptune at its current location seems unfavorable, are there dynamical obstacles to the capture of Pluto and the Plutinos under this scenario? Or are there features of the Neptune-Pluto system that would allow us to preclude this possibility of Neptune forming near its current orbit? Levison & Stern have examined the effect of the purely gravitational interactions of the giant planets on Pluto and concluded that the most important dynamical aspects of the Neptune-Pluto system could be reproduced. The exception was the amplitude of the 3 : 2 resonant argument, which was found to be too large in their model. We performed simulations of the outer solar system that included a slowly accreting Neptune and found that the efficiency of capture of dynamically cold particles into the 3 : 2 resonance was increased by a factor of 3, and that the resonant argument was substantially decreased. However, further dissipation is still required to match all aspects of the Plutino population and to produce truly Pluto-like orbits. Given that cold initial conditions did not reproduce the observations completely, simulations of initially dynamically hot particles near the 3 : 2 resonance with Neptune were also examined. These results, though resulting from seemingly ad hoc starting conditions, are reported as they produce remarkably good matches with both the Plutino population and Pluto's own orbit, including all three of its known resonances. These simulations reveal that Pluto could have arisen from an initially low-e (~0) but high-i (~25°) orbit, both a clue to its origin and an illustration of the difficulty in understanding Pluto's current orbital configuration.